Additional Conditions For Successful Appeals
An erroneous conclusion of law is a starting point. And, usually at least one of the lawyers for the defendant, often a "second chair" junior lawyer when there is more than one lawyer, keeps of running list of potential appellate issues during the course of a criminal case and trial, to review in the short time allowed to decide whether or not to file an appeal and on what grounds the appeal will be brought, later on.
But this is really only a "brainstorming list" because several additional points are necessary for something to be a sound additional issue, in addition to merely making a mistaken statement of law in a hearing for there to be a good ground for an appeal
- As @DaleM noted, you have to preserve the issue in the trial court by bringing the error to the court's attention in a timely fashion. This is called preservation.
There are exceptions to this rule, primarily for "plain error" (e.g., the judge rules that evidence received on Tuesdays can't be considered by juries, or that aspirin is a Schedule I controlled substance, or that testimony from a witness about physical conduct that witness saw the alleged crime being committed personally is hearsay and excludes the witness), "structural error" (e.g. the grand jury in a state that requires them or in federal court only had six members when it is required by law to have 23, or the official called with summoning a jury pool intentionally excluded all Hispanic jurors because he presumed that they were all not U.S. citizens based upon their surnames), and a court's lack of jurisdiction (e.g. a state prosecutor brings federal mail fraud charges in a state court, or a felony case is tried in a city court only authorized to hear misdemeanor cases). But those are rare exceptions to the general rule that almost never happen in urban courts in Northern states, but sometimes come up in rural courts and courts in Southern states where compliance with the constitutional and criminal procedure rules is often more lax and sometimes the judges don't even have law degrees (these kinds of problems are comparatively commonplace in proceedings before Justices of the Peace in New York State, for example).
- The error has to be causally related to an incorrect conclusion. A trial court judgment can be affirmed if there is any legal theory that would support the judge's conclusion, even if it isn't the actual reason that the judge did reach that conclusion, and despite the fact that the prosecution din't preserve that issue in the trial court.
For example, suppose that the judge was wrong about the tampering being a grounds for probable cause, but the mechanic who was in lawful possession of the vehicle at the time gave the officer permission to search the vehicle, even though no one thought to raise that argument in the trial court. The judgment would be affirmed even though the judge's ruling was based upon an erroneous interpretation of the law.
- In evaluating whether or not the trial court's decision on the suppression motion was was erroneous, the court's conclusions regarding the facts are taken as true by the appellate court, unless there is no evidence that was presented at the proper time in the trial court that supports that finding of fact and no reasonable judge could infer that finding of fact from the available evidence.
Also, since most decisions made by trial court judges in criminal cases are really mixed questions of fact and law that involve an application of the law to the fact, and most of the relevant laws, like what constitutes "probable cause" involve some exercise of judgment by the judge rather than being clear black and white rules, these decisions are usually reviewed for "abuse of discretion" by the trial court judge, although a decision that can be reached only based upon an error of law is, by definition, an abuse of discretion.
Basically, if a ruling was a close call and a reasonable judge could come to a different conclusion than the appellate judges would have come to, in good faith, then the trial court judge gets the benefit of the doubt.
These considerations are called the standard of review. Abuse of discretion is most common in criminal cases, but it isn't the only one.
There are some issues that truly are pure issues of law. For example, maybe an to the stolen property law to include data on flash drives when the flash drive itself isn't stolen, just the data, was only enacted effective for cases filed after July 1, 2020, and the judge applied this statute to a September 20, 2020 trial, even though the case was filed on June 1, 2020. There is no discretion for the trial court to exercise and the facts can be determined from the clerk of court's records without looking at any actual evidence in the case. Pure issues of law like that are reviewed by the appellate court de novo which means that the appellate court ignores what the trial judge did and just tries to determine the right answer and finds that there was an error if the trial judge got it wrong.
- The incorrect conclusion must not have been "harmless error" which means (in the context of a criminal trial on the issue of guilt or innocent) that one cannot be reasonably comfortable that the error did not change the outcome on ultimate conclusion that the defendant was innocent or guilty on one or more of the counts upon which there was a conviction. (Acquittals can't be appealed by the prosecution even if they are based upon some clear legal error or are not supported by the evidence offered at trial.)
For example, suppose that the defendant is convicted based upon evidence obtained in the search of the car that genuinely was unlawfully obtained and that objection was preserved with a timely motion raising that issue in the trial court. This might be reversible error. But not necessarily.
Suppose that at the same moment that one cop was searching the car (unlawfully), that another cop was searching the defendant's house pursuant to a search warrant based upon a tip that the cop got from the next door neighbor a few hours earlier (and hadn't told his colleague about so that it was not fruit of the poisonous tree), and that search also turned up stolen property. Then, both examples of stolen property were admitted at evidence at trial, after which the jury entered a verdict of guilty of possession of stolen property (which was a crime defined in a way that would result in one conviction no matter how many items were stolen). In that situation, the incorrect ruling on the suppression of evidence from the search of the car is "harmless error" and the conviction would still be affirmed.
A presumption that makes clearing the harmless error barrier harder is that a jury, when there is a jury verdict, is presumed to have made any conclusions that were necessary to support the verdict, even if you know from talking to the jurors themselves after the trial is concluded, that this wasn't actually their reasoning.
- The defendant's appeal has to comply with the procedural requirements for filing and perfecting an appeal.
For example, there is a jurisdictional deadline to file the appeal. There may be a filing fee that had to be paid if the defendant was not indigent or was indigent but didn't ask for permission to have the fee waived in a proper motion with financial disclosures about the defendant. And, the defendant is required to do what is called a "designation of record" within the deadline for doing so which means making arrangements to have transcripts of the relevant hearings prepared (at the defendant's expense unless the defendant secured a waiver of this cost because the defendant is indigent) and giving instructions to the clerk of the court regarding the exhibits and materials in the clerk of court's record that have to be transmitted to the court of appeals with the proper file number.
Then, the defendant has to file an opening brief in the appeal by the deadline for doing so, and that brief is subject to rigorous requirements regarding length, formatting, properly cited references to all legal authority relied upon to show that the defendant is right, and properly cited references to the transcripts, exhibits and case file provided to the court of appeals for all factual matters necessary to establish grounds for an appeal.
Then the prosecution files an "Answer Brief" addressing the points raised in the Defendant's Opening Brief, then the Defendant writes a shorter "Reply Brief" in response to the points raised in the "Answer Brief", then sometimes there are oral arguments before the panel of judges deciding the case, and then you wait (sometimes several years) for the panel of appellate judges to decide if any relief should be granted in the appeal and why.
The prosecution or the defendant, if unsatisfied with the appellate result, can appeal it further to the supreme court to which the intermediate court of appeals reports, in most cases, and while those further appeals are discretionary and rarely granted, they can take many more months for that process to be briefed and for the higher court to make a preliminary decision. If the case is in state court and the appellate issue raises a question of federal law (usually a constitutional right), one more discretionary appeal to the U.S. Supreme Court is also allowed.
If the appellate courts get it wrong on direct appeals sufficiently badly, or if there is a ground for setting aside an appeal that isn't apparent on the face of the information that the appellate court may consider that was presented in the trial court in connection with the original trial, such as ineffective assistance of counsel behind the scenes, this can be raised in what is called a "collateral attack" on the conviction, rather than a direct appeal, but that would be very unusual in the kind of plain vanilla erroneous statement of law by a judge in the course of a hearing or trial of the type described in the question.
Bottom Line
In conclusion, a trial court making a mistaken statement of law is a starting point which is one of the main grounds for appealing a criminal conviction. But there are many other substantive and procedural hurdles that must be overcome to actually have a fruitful appellate issue.
Types Of Relief Granted On Appeal
About half of cases that actually go to trial before a jury and produce a conviction, rather than being plea bargained, are appealed and typically about 10% of appeals are successful in securing some relief (although often not dismissal of all charges of conviction; partial relief dismissing some charges while affirming others, adjusting a sentence for one or more of the charges, or ordering a new trial on one or more of the charges, is far more common).
Of course, your mileage may vary, the percentages and probabilities given are merely typical and vary from court system to court system, and by type of case, and by type of appellate issue raised.
Most commonly, if the appellate court grants relief, it will vacate the conviction and to remand the case for a new trial in a manner that complies with the appellate court's directions about the legal issue upon which it reversed the conviction (if there is an error on an issue like suppression of evidence, and the evidence not suppressed was very important evidence but not the sole evidence presented in the case supporting a conviction or from which reasonable inferences could be made which would support a conviction) in the simple case of a single charge of conviction (where the appropriateness of the sentence assuming that the defendant was indeed guilty is not in dispute).
After that happens, there are usually further plea bargaining negotiations, and if those don't conclude the matter, then the prosecutor can either drop the case, or take it back to a new jury trial, usually quite promptly because all of the other steps to get the case ready for trial from prosecution disclosures of evidence to arguments of what is admissible evidence to jury instructions, to selection of witnesses have already been worked out. The prosecution and defense and judge need to work together to schedule a new trial date (usually an easy thing but a nightmare in the days of COVID) that is far enough out to allow witnesses who need to be recalled for the new trial to be placed under subpoena (or for transcripts to be designated to use in lieu of live testimony if the witness is no longer available), and everyone is off to the races on a much quicker schedule than a new criminal case of the same type starting from scratch.
Conviction rates in retrials tend to be only modestly lower than conviction rates in other criminal trials (typically closer to 50-50 rather than well in excess of 50% in first trials held before an appeal) but are hardly a sure thing for either side - mostly because cases that aren't close usually get plea bargained rather than going to trial. The conviction rate at a first trial is usually significantly over 50% because most defendants are indigent and have free public defender counsel if they go to trial and are in jail in the meantime either way, and because many defendants are overly optimistic about their odds of success in their own cases (which are stronger than average of they would have taken a plea bargain).
A variety of not strictly legal considerations go into determining how hard the prosecution will press the case following an appeal. The severity of the crime, the convictions and sentences (if any) that were affirmed on appeal, the resources of the prosecutor's office and law enforcement to take on another trial, the strength of the case when the error is corrected on appeal, the pressure being received from the victim, the publicity that the case has attracted, the priorities and agenda of the district attorney, the availability of witnesses and evidence for a new trial, the attitude of the defendant, the amount of time already served in the process by the defendant prior to conviction and/or while awaiting an appeal outcome, all figure into this analysis.
The constitutional and statutory right to a speedy trial give the prosecution a pretty short deadline to decide what it will do on remand from the appellate courts to the trial court when the appellate process is concluded.