Deliberate mistake: When the Doctor begins to "fade" in the transporter room his mobile emitter fades with him. Since it's made of solid matter and is not a hologram, this shouldn't be possible.
Continuity mistake: Xena leaves Darius' house, where she forgets her chakram. Then there's a shot of her riding Argo, with the chakram attached to her hip. Later Darius shows up to bring the 'missing' chakram to her.
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.
Well Bargained and Done - S1-E2
Character mistake: Tybus says he has a lance of 5 mechs. In Battletech, a lance is 4 mechs. While a Clan star does have 5 mechs, Tybus is an Inner Sphere character.