That is the entire purpose of the appeals courts. And in the case of Greer, the 2d CA was actively involved. Under no circumstances should a poll be taken to assist in the determination of the legality of a judicial decision. The fact that most people do not like a finding of fact is irrelevant, and rightly so. That would be called mob justice. There are two solutions if the judicial reviews do not seem to satisfy, impeachment or not reelecting the judge.
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.