Continuity mistake: When Sid opens the box from the fireworks company and takes out the rocket, he pushes the large corrugated box towards the window, but when Sid puts the milk crate with Woody onto the table that large box has vanished.
Continuity mistake: When Andy's toys see Woody holding Buzz's severed arm they abandon him, and Slink drops the window blinds while Woody's leaning out Sid's window that's still open, but when Woody turns around to see Sid's mutant toys start working on Buzz, Woody jumps off the table and suddenly that window is closed behind him.
Other mistake: After throwing Woody to the floor, Sid raises the window shade and tries to burn a hole in Woody's head by using a magnifying glass to focus the sunlight. Sid is leaning over Woody with his back toward the window and yet he does not cast a shadow on Woody. In addition, the position of Sid's body would block the sun's rays from hitting the magnifying glass but the close-up shows the narrow beam of light hitting Woody's head.
Factual error: In the scene when Buzz and Woody are at the gas station, Buzz looks up at the moon and talks about Zurg. The reflection of the moon on his helmet looks the same as the moon in the sky, rather than its mirror image.
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.
Audio problem: When Andy is in his cardboard Buzz costume, and says "Buzz Lightyear to the rescue, " his mouth doesn't move.
Continuity mistake: Before the staff meeting, when Woody gets his doodle pad we see the outlet under the crib, but then the outlet vanishes, and reappears later.
Continuity mistake: When Buzz wants to prove that he can fly, he jumps off Andy's bed and ends up on the loop car track, and the three stacked wood blocks (letters A, C, E) suddenly appear in front of the wicker hamper between shots.
Continuity mistake: When Buzz watches the TV commercial and realizes that he's really a toy, by the time "Al's Toy Barn" is mentioned and he reads "made in Taiwan" on his arm, one of the soda cans on the floor changes its position and the trash bin with the crumpled paper around it vanishes.
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.
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.
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.
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."
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.