[0]: https://deathpenaltyinfo.org/policy-issues/innocence
EDIT: Oh boy that rabbit hole is deep. So here's some _potentially_ innocent people who have been put to death[1]. None of those are actually proven to be innocent, but there is at least some amount of evidence that spells reasonable doubt on their conviction.
[1]: https://deathpenaltyinfo.org/policy-issues/innocence/execute...
It took a matter of minutes to find that Toforest Johnson was successfully convicted of murder based on somebody claiming they overheard him confessing. The prosecution had concealed from the defence the fact that they paid this witness a substantial sum of money. That sort of bullshit shouldn't work to give somebody a traffic ticket, never mind a death sentence and yet sure enough US courts thought that was good enough.
So you are OK with a a few mistakes, as opposed to many?
Point is also that it is possible that a mistake will be made. We know wrongful convictions have occurred, including for those on death row.
[0]https://deathpenaltyinfo.org/executions/2021