
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.

Continuity mistake: When Donna jumps off the bridge, it's into relatively shallow water under the bridge, and there is land very nearby (at both ends of the bridge). When the camera shows her in the morning, she is suddenly far out to sea in the ocean. (00:01:51 - 00:09:33)