Appeals courts don't look at evidence except to determine whether a decision would be reasonable if all of the evidence favoring it were viewed in the best possible light and all of the evidence opposing it were viewed in the worst possible light. In the scenario I posited, an appeals court could uphold the trial judge's decision on the basis that there was one expert who thought the will was authentic, and the trial court judge might have had some reason to believe that witness over all the others. Further, the trial court judge might have had some reason to believe that the supposed samples of the decedent's writing supplied by the other heirs were fake even if they were on seemingly-valid notarized documents.
I would further posit that, in many cases, the idea of having ordinary people look at evidence and decide what they think of it is not usually called "mob justice", but rather a "jury trial". There are, to be sure, some cases where ordinary people lack the knowledge and judgement necessary to make intelligent decisions (e.g. in a medical malpractice trial, if the plaintiff claims the defendant should have done some procedure which is commonplace, while the defendant claims the procedure has been considered obsolete since 1938, there's no way a jury not familiar with medical practice would know who to believe--especially since both sides might be telling the truth). Nonetheless, a group of 12 jurors is less likely to consist entirely of people who can't smell a rat than a 'group' of one judge.
The 2d CA , as I mentioned previously was very involved, and after its first decision upholding Greer in 2001, it subsequently sent the case back to Greer after a subsequent appeal, and again heard "new evidence" from the Schindlers in October 2001 whereupon it directed a 5 doctor review. After that, in 2003 the chief justice of the 2d CA ordered the guardian ad litem to prepare a report, which as we all know was favorable to both Greer and Michael Schiavo. So in this case at least, the appeals court was quite active.
I would further posit that, in many cases, the idea of having ordinary people look at evidence and decide what they think of it is not usually called "mob justice", but rather a "jury trial"
The question was posed as "what do you do with a judge when most people disagree", which would be polls or mob rule. In any case, the guardian ad litem certainly would fall into your category of ordinary and independent people. So why should a jury find any differently?
Nonetheless, a group of 12 jurors is less likely to consist entirely of people who can't smell a rat than a 'group' of one judge.
You mean like the O.J. or Robert Blake juries? But in any case, if states so believe, then state laws should be changed to reflect a need for jury trials when dealing with evil judges. But in no case should the federal government be involved.