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: When Tom is locked up in an institution for the mentally ill, he is given a bed on a mixed gender ward/wing (both men and women). Wings and wards in mental institutions have not been mixed gender for more than 100 years - it is inconceivable that this practice would be existing in the 1990s in a large city in the USA.