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.
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.
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.
Audio problem: The scene where Tom goes to his home, to be confronted by his wife, the dog, and another man holding a shotgun. The other man has just told Tom that either he walks away or he gets shot in the leg. There is then the sound of the dog growling for several seconds, but the dog's mouth/muzzle isn't moving, and it isn't growling.