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.
Character mistake: Mrs. Reynolds, the housekeeper at Pemberley, refers to Mr. Darcy's late mother as Mrs. Darcy while showing Elizabeth and her aunt and uncle the house. This is a grave mistake on the part of the filmmakers as she should have been referred to as Lady Anne, the way her sister is known as Lady Catherine. Their father was an Earl, making them Ladies by birth, not by marriage. Hence, they must be called Lady followed by their first name.
Continuity mistake: The paint on Sonny's face (from painting their living room) changes position after him and Sasha go to the shops.
Continuity mistake: In the episode where they are on strike, Oswald says he gets a job with Global Postal due to the Christmas season rush, but, he was already working for Global Postal in the previous episode.
Revealing mistake: The eyes of the actor playing Gideon the robot can be seen through the eye slits of the robot mask in some shots.
Visible crew/equipment: When Donna jumps off the bridge, her falling body is a dummy/mannequin of some sort - its arms are stiffly by its side, and it has no face. (00:01:54)
Factual error: In this final made-for-TV mini-series of the 'Lonesome Dove' franchise (the one with James Garner as Woodrow Call), they show the crazy renegade teenage killer hanging Judge Roy Bean from the beams outside the front of his own store/courthouse. Bean died peacefully in his bed on March 16, 1903, after a bout of heavy drinking in San Antonio.