Appeals and Innocence Project type data should give some idea. Some states even have official programs to investigate peoples innocence after conviction. So it definitely happens more than it should and there should be some data out there.

From my personal experience, it seemed like everyone I dealt with who was part if the system was either incompetent, made mistakes, or might have even been covering things up. The trooper I already mentioned. The corporal investigating him said the trooper's lie was just a misunderstanding, but offered no reasoning or evidence to support that. He also overlooked some other things that were violations of policy (they only cited him for one reg when he fit several). The Sargent who approved the citation said he couldn't do anything about it even if it's incorrect, which is wrong because he can take action based on what the LT told me later. The LT investigated a follow up complaint (the trooper never took the corrective actions listed in first complaint). He didn't follow the correct complaint procedures since he closed the complaint without any notes or findings. I had to call IA, then I assume IA called him since the LT called me a day or two later. He can't even answer basic questions like what laws he used to determine the rules of criminal procedure weren't broken and if he investigated the trooper's conduct as prosecutorial misconduct since he acted as the prosecution and knowingly held an incorrect charge and made several misstatements in court (that we have evidence for). The first magistrate we got gave a continuance. He was arrested on unrelated charges. The second magistrate gave another continuance and thought that we were calling him prejudice when asking to dismiss with prejudice (most magistrates in my state are not lawyers). The third magistrate was a retired police cheif who showed bias, wouldn't let us present a motion, misapplied the law, and was yelling at us to the point his face turned red and he was not understandable due to a lack of air. The ADA originally assigned to the case had an email complaint and the information to confirm that the trooper knew this was an incorrect charge and that the citation didn't even claim the elements of the offense were met, yet they took no action and allowed us to be subjected to those pretrial restrictions. At the appeal, the new ADA tried to misapply the law, with some success. They also told the court administrator/scheduling not to talk to us and not to accommodate any of our witnesses without their approval, which normal for other types of cases with standard discovery procedures, but those don't apply here. The judge actually contradicted his himself in some of his reasons for his determinations - at one point saying a trial de novo is a complete do-over so he won't allow any record from that trial to be used and later saying you would need a record of the previous trial in order to have the charge dismissed. He then misapplied the law and would not even look at, or accept as evidence, an official letter from a state agency that helps define an ambiguous term in the law, which would show us to be in compliance with the law. Even without the letter, the principle of lenity and the rules of statutory construction were blatantly ignored. There were also some paperwork and administrative mishaps, like some information not being recorded and later spending 30 minutes on a moot motion, or the court refusing to provide us with the amended citation with the new charge because "we don't have anything to give you" eventhough it's in the file. The other party was in violation of two similar laws the this one, yet the trooper and DA office decided not to investigate/prosecute even when she admitted being in violation for one offense. So much for the law applying equally.

So yeah, in my view the system has no integrity and is severely broken. I have little faith in justice actually being carried out. I guarantee many people have been convicted who were innocent. I think it's mostly due to the fact that innocent until proven guilty doesn't exist anymore.