I feel like throwing out some more details, also making the point that I am not a lawyer. I welcome any corrections to my assessments.

On appeals, the court can find that there was an error in the interpretation of the law or the legal process, and also find that the error did not rise to the level of substantially impacting the verdict (whether it was a jury trial or a bench trial). In such a case, the lower court’s verdict stands.

Now, let’s say we have a criminal appeal where, during the appeal case, it is demonstrated that (for example) the police investigation was horribly shoddy or outright corrupt, and this is new information which has been more completely demonstrated after the initial verdict. This would be the rare situation where the appeals court would address a matter of fact, as in “the facts of the initial case were incorrect or incomplete.” In our hypothetical, the appeals court finds that, yes, the failure of that information being revealed in the original case would have had an impact on the verdict, so the appeals court “overturns” (voids) the original trial.

At this point, the District Attorney needs to decide whether to retry the case. Choosing to retry the case does as I described above - everyone starts over. And it is still possible for the defendant to remain in detention pending a verdict. The new trial, with its new jury (or judge), having access to the additional information about the handling of the investigation, now comes to its own decision, ideally separate from the previous trial procedure. If the defendant is now found not guilty, the defendant is freed from any consequences - and may have grounds to file a civil suit against police or the state for their “inconvenience.”

Or, the DA may look at the new information and decide, no, we are not going to pursue these charges any further, because the likelihood of achieving conviction is too low. There are other political implications which may come into play, as District Attorney is an elected office (in most places? in every place? not sure). In this situation, the defendant’s charges being dropped, in the eyes of the law, it is as though the defendant had never been charged with a crime. As above, this person (notably not a defendant) may have grounds for a civil suit.

The other thing about appeals courts (at least federal appeals courts, may be the same or different in various states) is that the first appeal goes before a subset of the entire appeals court panel, generally three judges. If that three-judge panel does not find in favor of the appellant, the appellant can request that the appeal be reviewed en banc, or by all appeals court judges (likely at least seven). I believe that the en banc court can simply review the initial appeal case and affirm the decision there without having to actually hear the case again.

I hear you, but these are the judges he’ll be appealing to

https://www.nycourts.gov/courts/ad1/