Factual error: In the whole episode, Romania is depicted as a monarchy with the king in a position that allows him to make political decisions. However, Romania ceased to be a monarchy in 1947. By the time depicted in the episode (circa 1997), Romania was a republic and its head of state was the president. Members of the ex-royal family did not hold any positions in the Romanian government and were certainly not authorized to represent Romania in international events.
Plot hole: When the radar man of the USS Cayuga describes a radar reading to likely be "One of the Russian cruisers", the commanding officer of the USS decides not to pursue it saying, "We are after bigger fish today - I want the Vasilyev". In the film, the Vasilyev is depicted as a destroyer, which is a smaller and lighter ship than a cruiser. In this context, the cruiser would be a "bigger fish" than the Vasilyev and the CO should pursue it instead if he was after the larger, more dangerous vessels as he seems to declare.
Continuity mistake: When Lt. Roberts is held hostage in Admiral Chegwidden's office with the Admiral and the Major, he mentions a sister named Winifred. She is never mentioned again throughout the series. In later seasons it is implied that Lt. Roberts only has one sibling, a brother named Mikey.