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.
Factual error: Enlisted soldiers are shown saluting each other, as well as addressing a sergeant as "sir." Enlisted personnel in real life never salute each other, nor are NCOs (like sergeants) ever addressed as "sir."