Judges in US courtrooms famously use a gavel at appropriately dramatic points in a trial. If a judge fails to use a gavel, or uses it at the wrong moment, is this legally significant? Or is the gavel purely ceremonial?
It is purely ceremonial. The tendency in modern jurisprudence is towards the practical and away from legalisms and technicalities. Even if a judge used a gavel in some way inappropriately, it would be unlikely to have any legal significance for anyone but the judge.
An argument based on gavel misuse would fall into the "fringe-on-the-flag" category of legal arguments (yes, there are people who think that the court's powers are determined entirely by the fringe on the courhouse flag). The gavel is a traditional trapping of a common law courtroom, but has no legal significance.