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.
Paradise on Your Doorstep - S1-E5
Factual error: The plane Tom hijacks is a Grumman Goose. This has a maximum altitude of around 20,000 ft. When the pilot flips the pressurisation switch, the instrument panel shows the plane is only at 2500 feet! The cabin wouldn't have depressurised at such a low altitude - and even had it done so if the plane had been flying much higher, it wouldn't have had such a severe and debilitating effect so quickly on Tom as suggested in the episode - he passes out in about 3 seconds.