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.
Other mistake: The Sliders discover the reverse-time issue when they notice that the clock on the wall is backward. However, in other shots, clocks look normal. Look carefully at the clocks on the judge's desk as the camera pans by.
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.
Cigarettes and Alcohol and Rollerblading - S2-E8
Visible crew/equipment: When Ted and Dougal look into the window of Dick Byrne's house, the rope pulling Father Cyril's skateboard is visible. (00:21:50)
Continuity mistake: The paint on Sonny's face (from painting their living room) changes position after him and Sasha go to the shops.
Attack Of The Mutant (1) - S2-E2
Other mistake: In part 2, it was revealed that Libby was really the Masked Mutant all along but, in one scene in this episode, Libby is sitting next to Skipper while the Masked Mutant is standing on top of the bus.
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.
Factual error: The Strikers steal several suits of Elemental armor in a few minutes and use it to escape after they are discovered. It takes 15 minutes to put on battle armor unaided and that's for an Elemental trained in its use. The armor is custom fit for a 6 and a half to 7 foot Elemental but 5 foot Val wears one. Elemental armor is also protected by voice recognition and code phrase software. Needless to say there's no way they could just walk out with 3 suits.
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 the officers are practising with the riot gear, the reflections of the studio lights are frequently seen in the shields.
Caroline and the Used Car Salesman - S3-E11
Continuity mistake: In the first scene with Richard at the used car lot in his initial job interview you can see his name already written on the employee file cabinet behind crazy Fred. Later he uses the cabinet to get a gift he had bought for Caroline.
Revealing mistake: When Matthew is sliding backwards because his shoes are icy, just before he falls you can see the board he was on to allow him to move backwards. (00:02:00)
Factual error: Tom finds a notecard with an "internet access code" that is an IP address: 271.287.291.31. The problem with this is that IP addresses cannot go above 255 as the starting three digits - it's a completely invalid address.
Continuity mistake: There are two Bristles shown to be in attendance at the ball: one in a tuxedo and one in his normal clothes. (00:06:30)