Continuity mistake: In the original Toy Story Sid uses a magnifying glass to make a permanent burn mark on Woody's forehead. This seems to have disappeared for Toy Story 2.
Suggested correction: It's also disappeared in the final scene of the first film. Presumably, Andy or his mother were able to have Woody repaired at some point between moving and Christmas arriving.
Continuity mistake: When the Toys enter Al's Toy Barn looking for Woody, the colour of the tiles right after the cashiers don't match between the aerial and close-up angles.
Continuity mistake: Woody's height slightly changes in the scene where Buzz tries to convince him to return with them. You can notice that from the scene where Woody starts to explain why he doesn't want to come back, and in the one where he turns away and keeps his arms folded.
Continuity mistake: In the baggage area when Woody fights with Pete, his arm is torn (an injury which had previously rendered it useless). However, in the next scene going to rescue Jessie, he is using the arm freely and there is no sign of a tear or fix. There is then reference (and visible signs) later in the film that the arm has been fixed.
Continuity mistake: At the beginning of the movie, Buster knocks over the Troikas (the toys that fit inside each other), but they vanish a couple of shots later. We can see that they aren't behind Buster when he sniffs the bedroom and heads near the Potato Heads.