Other mistake: When Andy's friends show up all of the Caucasian boys have Andy's face and hair. Most surely due to the limited technology available then, but weird nevertheless.
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 looks at his foot and sees ANDY written on it, at first it's sloppy and a bit backward with a misshapen A, but when the angle changes it's a lot neater. (00:22:05)
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: The objects on Hannah's play table change position between two consecutive shots. Most notably Buzz's arm holding the teapot, as well as Buzz's legs. (00:49:20)
Continuity mistake: When Woody opens the back door on the moving van, the ramp handle is black. But when Rocky Gibraltar uses it, it is red.
Continuity mistake: In the opening scene in Andy's room, Woody's expression is semi-smiling with his mouth closed. Then, when 'You've Got A Friend In Me' plays and Andy takes him out of the room, Woody's expression changes to a blank stare with his mouth semi-open. When Andy returns to his room and places Woody on the bed, his expression is back to the first one with mouth closed. It was not established yet that Woody was 'alive', so his expression shouldn't have been changing at this point.
Continuity mistake: When Buzz and Woody escape the rocket, and fall down, Buzz has tape on the front. But next shot the tape is not there.
Character mistake: Mr Potato Head gets torn apart by baby Molly after the opening scene. When Andy returns to the room with Buzz everyone resumes their positions, but Mr Potato Head looks for his bits and sits under the shelf with the other toys.
Audio problem: When Andy is in his cardboard Buzz costume, and says "Buzz Lightyear to the rescue, " his mouth doesn't move.
Continuity mistake: Near the start, when Woody mentions the party being moved to today, there are 2 black spots on the wheel by the toy box that change place. Note the spoke of the wheel.
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 Andy and Woody start spinning in the recliner, Woody inclines to the center (to his right) instead of inclining to the left according to the centrifugal force physical law. (00:02:56)
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.
Suggested correction: The sun is concentrated further beyond, not the helmet, so the helmet doesn't get as hot from it as that area does. Besides, plastic doesn't melt that easily, not from a concentrated sunbeam at least. It's a better question to ask if plastic can concentrate light as much as a magnifying glass can. We don't know when the toys feel something, so he must have felt the heat before it damaged its hand. We hear sizzling but that can only be superficial. No scar is from Sid's torture either.
