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.
It's Not Such a Wonderful Life - S1-E12
Continuity mistake: In the previous episode, Tom was shot and had a scar from the resulting bullet wound. In this episode, when he takes his shirt off on Christmas Eve while talking to Alison, the scar tissue has completely vanished. Bullet wound scar tissue - even after years - doesn't completely vanish. It's been less than months since the previous episode.