Continuity mistake: In the scene where toys in Sid's room make their first appearance, they crowd around the middle of the room and pull at Janie's body and the Pterodactyls head. The shot cuts to Woody on Buzz looking horrified. When it goes back to the toys, they're dragging a different dolls body away (the same one that is seen sitting for tea with Buzz in Hannah's room in a later scene). (00:40:50)
Continuity mistake: When Buzz and Woody are riding RC, holding onto Slink in the end, there's a shot where the truck turns to the left on a bend. Slinky gets stretched further, and RC goes off to the right side of the road due to centrifugal force. We can see that RC is going to go under a parked car. The camera switches to the front and we see the car pass from further right. They never end up going under it and tangling Slinky in the wheel. (01:12:00)
Continuity mistake: Towards the end when Potato Head and Ham are playing Battleship and Woody is yelling from Sid's room, Buzz is wearing the apron that Hannah put on him. He's wearing it throughout that whole scene except when the toys in Sid's room are fixing him and Woody says; "you're not gonna eat him, you monsters."
Continuity mistake: When Woody plans to knock Buzz behind a desk, if you look closely at the globe in a box next to the bulletin board, it is slightly off-position in its stand. Later, when the bulletin board begins to fall on the globe, the globe is positioned correctly. (00:24:40 - 00:26:00)
Deliberate mistake: The license plate on the back of Andy's car says A-113, while the license plate in the front of Andy's car says A-111. A deliberate nod to room A-113 at California Institute of the Arts, often used by alumni, but a mistake regardless.
Factual error: When woody lights the rocket using Buzz's helmet to refract the sun, Buzz being made of plastic (including his helmet) would've been burned or at least had some sort of damage from the sun, but he doesn't. The same when Woody finds out his hand is burning. No visible burn mark.