In several episodes when Denny and Alan are looking to join (and actually do join) a branch of the military, they choose the Coast Guard Auxillary, to which the show mistakenly refers to as "the Auxilliary Coast Guard".
Throughout the series, Alan Shore and Denny Crane sit on the balcony overlooking the city of Boston. However, during the cold winter months, you never see the breath of either character, thus demonstrating that the "balcony" is part of a set, and not an actual location.
Throughout the series, there is an inconsistency in the proper courts for the proper cases. For example, there are certain criminal cases - which would be heard in state courts - in which the set being used was the Federal Court set with the seal that says "District of Massachusetts". In addition, several judges switch between the state court and federal court sets while state court judges and federal court judges are separate and independent.