In the Amanda Knox case in Italy, two things stand out about the recent acquittal. First, the court appointed its own experts to analyze the questionable DNA evidence which was used to convict her on the first go-round. This seems an idea the US should use more. Certainly there are instances in which a court will appoint what is called a "special master", who is someone assigned to look into the facts and report back to the court on his or her findings. But in the context of a criminal trial, it is unheard of as far as I'm aware.
Second, the appeal saw a jury seated and evidence presented, just as in the original trial. In the US the appellate court would never be allowed to examine the facts and reach a different conclusion, as was done in the Knox case. Rather, the appellate court would have to rely on the trial court's factfinding, and limit itself to determining whether any questions of law were wrongly decided in the lower court.
It seems that in certain situations, where there is genuine doubt about the fact-finding in the lower court, that an appellate court *should* be free to conduct a full-scale re-examination of the facts, in order to reach a just result.
Probably many Americans are bashing the Italian justice system about now, but let's remember that in the end they got it right and achieved justice. Given the sorry performance of US courts in recent death penalty cases, we might learn something from the Italians.