Encounter at Farpoint (1) - S1-E1
Revealing mistake: When Q freezes Torres on the bridge, it is easy to tell that directional hoses were used for the effect. (00:06:25)
Character mistake: Throughout the entire series, the Turtles are referred to, by others and by themselves, as amphibians. But turtles are reptiles, not amphibians. However they are amphibious, amphibious reptiles.
Other mistake: When LB comes into Tweeg's room and he sees him covered in spots and he is discoloured he freaks out. Why does he freak out? He just saw Tweeg in the previous episode all covered in spots so he should know that it's him.