Do appeals court judges consider the reasonableness of the verdict in assessing prejudicial factors?

Suppose a argument on appeal is that there were prejudicial factors involved in the trial. Some or all of the jurors were possibly biased based on whatever reason, such-and-such evidence or testimony was too prejudicial and shouldn’t have been admitted, and so on. Does (or should) the appeals court include their own assessment of whether the verdict was reasonable in light of the evidence in assessing whether the prejudice (if any) was likely to have swayed the jury verdict?

Do they say “it’s hard to imagine how the jury could have arrived at that verdict based on rational consideration of the evidence alone, so it makes sense that they were inflamed by some emotion or bias; ergo it’s likely that such-and-such prejudice was a factor”? Or do (or should) they ignore this angle and just consider the issue of possible prejudice purely in the light of what they would think in a vacuum (as the trial judge would have done at the time)?

You are mixing up multiple things.
*A finding that no reasonable trier of fact could have reached * is something which is liable to be set aside on its own (lack) of merits without or before any consideration of bias or prejudice.

Bias will again vitiate the proceedings on its own.

A piece of prejudicial evidence is one which should never have been placed before a jury. There the reasonableness of the jury’s finding is not being challenged, the question becomes that if this evidence (presuming for a second it is in fact prejudicial) was not placed before the jury could they have come to a different conclusion? If the answer is yes, then it’s a proper case for reversal and remand.

I don’t know the answer to your question in full, but you might want to take a look at the concept of reversible error. IANAL, but it would seem to suggest that some infringements against due process are so egregious that they warrant a re-trial on general principle, no matter the evidence. And it makes sense, because if you have attorneys, jurists, or jurors misbehaving egregiously in one way, it kind of calls into question the whole record of the trial.

I mean, sure, everything seems to point to the defendants guilt, including DNA evidence and rock-solid eyewitness testimony from people who supposedly knew the defendant beforehand but if you’ve got a prosecutor stacking the jury with a bunch racists and the judge didn’t seem to mind, can you really be sure that the evidence quite so rock-solid as the transcript implies when all that evidence went through the same prosecutor?

This. Very true.

A person is either innocent, or guilty. There is no verdict “kinda guilty” or “we’re not really sure” or “maybe the trial should have gone differently”. If there was any reasonable doubt, the verdict should be “not guilty”. It is the prosecution’s duty to prove the case beyond reasonable doubt, and the jury’s job to be reasonable men and women in judging the evidence. Those are the issues that the appeal court decide - was the process in accordance with the rules? Were the rules violated so badly that (a) the verdict was flat-out wrong, or (b) the case should be retried in accordance with the rules.

The judge does not get to second-guess the jury and go lighter because of his personal doubt.

I’m not mixing up anything (though it’s possible you could dispute my premises).

My assumption is that it takes a lot before an appeals court (or trial judge, for that matter) will simply toss aside a jury verdict, and that “a finding that no reasonable trier of fact could have reached” is a very high threshold. IANAL, but I’m pretty sure that judges are not supposed to set aside jury verdicts simply based on the fact that they personally think that was not the correct verdict. So that there’s a lot of room for a verdict where the judges think “this is not the verdict that we personally think the jury should have arrived at based on the evidence”, even while acknowledging that perhaps the jury simply disagreed with that assessment. Judges wouldn’t simply overturn the verdict on the basis that they disagreed with it.

But that’s before potential bias comes in. In that case, the judge had a decision to make about “will this or will this not prejudice the jury?” (or, frequently, “does the evidentiary value of this outweigh the potential for prejudice?”), or “does such-and-such fact (e.g. exposure to news coverage, political affiliation, personal history, etc.) imply that the jury would likely be prejudiced in one direction or another?” The trial judge had to make the call and he/she decided that it won’t.

Now it’s on appeal, and the question is “did the trial judge make the right call in assessing the likelihood that such-and-such might be prejudicial?”.

From a purely logical standpoint, the less you believe that the verdict is supportable based on facts and reason, the more likely it is that the jury arrived at that verdict based on some prejudice. So to the extent that you, as appeals court judge, believe that the jury’s verdict was wrong - even if not nearly to the point that you would simply toss their verdict - then you’re more likely to assess that the admission of such-and-such evidence/juror(s) is likely to have played a role. To the extent that you personally believe that the verdict is well supported by the evidence, then it’s more likely that the factor did not prejudice the jury.

The question then is whether an appeals court would/should think along those lines. From a logical standpoint, they obviously should. But perhaps the law is that they shouldn’t.

In theory, errors in criminal cases come in (at least) two types: “trial errors” and “structural errors”.

Many (most) errors are “trial errors,” which means they are subject to a “harmless error” review. That is, the conviction is upheld if the court is satisfied that the error did not actually affect the verdict (i.e., that it is clear, beyond a reasonable doubt, that the same verdict would have been returned in the absence of the error). Since you can’t actually know what mattered to the jury or know what would have happened, the reviewing court tends to do this by assessing the strength and nature of the other evidence: if the evidence against a defendant is overwhelming, then most trial errors will end up being “harmless.”

Structural errors, on the other hand, require the conviction to be vacated, period. The idea is that the error (by its nature) so badly infects the process that you cannot assess its effect (and that the error goes to the very integrity of the proceeding). It’s a relatively small collection of errors. The ones I can remember are the complete denial to counsel (and, as a corollary, denial of the right to self-represent) and the violation of the right to an impartial judge and/or jury. I think there are some (but definitely not all) jury instruction errors that are “structural.” In those contexts (which are few), the conviction must be vacated if the error occurs.
In your examples, juror bias (if proved) would probably be structural. Evidentiary rulings are probably “trial errors.” There are plenty of legitimate complaints about where the line between the two types of errors is drawn.
I guess to try to more directly answer the question: the analysis would go in two parts. Whether the testimony should have been admitted (i.e., whether the trial court committed error), would likely be assessed “in a vacuum”. Whether that error was harmless (or whether the conviction must be vacated) will necessarily require consideration of the evidence as a whole.

Edit:

Vacating a conviction because no reasonable jury could have returned the verdict is a different issue entirely. And is absolutely supposed to be pretty deferential to the jury.

Plus, most people seem to think an appeal is “I want a second opinion.” In fact, the appeal judges defer to the jury and judge in the original trial as much as possible, because unless they can re-hear all the evidence they cannot know for sure what drove the decision. As Falchion points out they are looking for failures of the trial - errors that may have caused the jurors (or judge) to reach the wrong verdict. They cannot say “you should have believed X, not Y.” They can say whether Y’s history of untruthfulness was appropriately admitted or hidden.

If there’s any doubt, generally they order a new trial, so the full range of evidence can be heard again.