Goof (continuity error): When Rincewind and Twoflower are on the rock next to the Circumfence, the string holding Rincewind's hat around his neck keeps moving from above his beard to below it between shots.
Goof (revealing mistake): David Bradley's (Cohen) teeth can be seen in several shots before Cohen gets his dentures.
Goof (revealing mistake): During the opening title scene, at the docks, several shots show a radio aerial and mast on the side of a building. (Electricity and radio are unknown on the Discworld.)
Goof (audio/visual unsynchronized): When Rincewind and Twoflower are tied back-to-back, Rincewind says that "if complete and utter chaos was lightning, then you [Twoflower] would be the sort to stand on a hilltop in a thunderstorm wearing wet copper armor shouting 'All gods are idiots'."; you can tell by the way his mouth moves, however, that he actually says 'All gods are bastards', which is consistent with how it is worded in the novel.
Goof (revealing mistake): When Rincewind pulls the sword from the stone and starts falling backwards, you can see he is holding the sword handle but with no blade.
Goof (revealing mistake): In one scene, Twoflower is offered a dagger, which he takes by the blade.
Goof (plot holes): The book and the notes about the secret passageway say to pull the third book from the right but the one that is pulled is nowhere near the third book from the right (or even the third from the left).
Goof (continuity error): Twoflower gets out his picture box to take pictures of the new worlds being born. When we see him and the others from behind Twoflower is in line with them, but when we see him from the front he is clearly far in front of the others