This is the most patriotic and uncontroversial Holiday and not the stuff of litigation. This is not to say that Independence Day has never been mentioned in case law. It has, in fact, given one party its day in court.
The case involved a commercial dispute over a 40-foot container of shoes. The motion that party brought seemed to have been filed a day late. That is, until the Court realized that one of the days between decision triggering the possibility of a motion and the filing of that motion was a Holiday – the Fourth of July. This added a calendar day to the count, making the motion timely.
It was a short-lived reprieve, however. It turned out the movant lost on the merits.