Continuity mistake: When Renton visits the Mother Superior and overdoses, we see him remove his belt to use as a tourniquet. He sinks into the floor and Swanney drags him out to a taxi. When Swanney drags him into the taxi however, you can see Renton's belt around his waist. Why would Swanney go to the trouble to put Renton's belt back on if he didn't even put his coat on for him?
Continuity mistake: In the opening scene where Spud and Renton are running from the security guards, the shot changes to behind them and there is a crowd of shoppers about 20 - 30 yards in front of them. The shot then changes back to the front as they continue running, but they never seem to reach the crowd in front of them.
Continuity mistake: In the scene where sick boy and Renton are in the park with the bb gun, Renton at some point tracks some runners with his binoculars. He has to move his binoculars drastically to keep up with them, but when you see his front, he's barely moved them at all. They don't do this with sick boy.
Continuity mistake: In the first scene of the hotel room where the big heroin deal is going down, there is no mirror over the sink. In the future scenes in the same room, the mirror magically appears over the sink, notably when Ren gets a drink right before leaving at the end.
Continuity mistake: When Spud wakes up to find some, er, "stuff" in his girlfriend's bed, he goes downstairs to where girlfriend's family is eating breakfast. The camera from behind the mother shows her eating a forkful of food, then an instant later (not even a second later!) from beside Spud it shows her eating the food again.