Deliberate mistake: When "Legs" lowers the Pez duck named Ducky down through the removed lightbulb hole, to ring the doorbell, the lightbulb housing is bigger than the hole but they bring it up through the hole to remove it.
Continuity mistake: When Buzz is in Sid's sister's room, Woody comes up to it disguised in the Christmas lights. He then leaves them beside the door before he goes in. When they leave the room, the lights are gone. Later the lights return when Woody goes to get them, but there are fewer of them.
Other mistake: It's been mentioned that Sid sets his clock for 8:25 and it goes off at 7:00. Here's some more errors for Sid's crazy clock physics. When Woody is saying "Psst" to Buzz from inside the blue plastic basket, the clock on the wall says 6:25, yet the alarm clock next to Buzz says 6:55. It goes off 5 minutes later and after Sid takes Buzz out of the room, the clock on the wall has changed to 3:10. When Woody is talking to Sid's toys a minute later, the clock now reads 10:00. The maximum amount of time that passed between the already wrong 3:10 and the 10:00 is 5 minutes. You can tell because Sid wanted to launch Buzz strapped to the rocket ASAP and Woody wanted to rescue Buzz from his current strapped-to-a-rocket state very fast.
Continuity mistake: When the army soldiers are yelling into the baby monitor that the kids are heading up to Andy's room, the baby monitor is right in front of Woody on the floor. Yet, when the camera pans out to show all the toys scrambling for their places the monitor is gone, and Hamm is right in front of Woody. Then, when the camera zooms back in to show Woody, the baby monitor has reappeared.
Continuity mistake: When Andy's mom suggests to Andy they go out to eat at Pizza Planet and that Andy can only bring one toy, Woody picks up the ball (the one that can predict things) which was next to him and asks if Andy will pick him. If you see in the earlier shots the ball wasn't there.
Continuity mistake: When Woody and Buzz are at the gas station and the big truck pulls in, Woody falls limp to the ground. The truck pulls over him, and stops with its tires an inch from his head. In fact, the brim of Woody's hat sticks up into the space between the two tires. In the next shot when Woody scrambles out from beneath the tires, his head is directly under the tire to our right.
Revealing mistake: When Woody falls out of the closet wrapped in the string lights he hears Buzz's voice, and in the next shot as Woody sneaks up to Hannah's room we see Sid's open door and doorway, which looks perfectly normal. However, after Woody rescues Buzz from Hannah's tea party they both stop in the hallway, and there's another shot of Sid's open door and doorway, only this time it's not normal to say the least. All six of the latches, bolts, and locks that are normally attached to the inside of Sid's door are now actually kind of floating there in mid-air right beside the doorway, as if there's an invisible door there. Weird that Pixar artists deliberately did this, but it's bizarrely funny to see.
Continuity mistake: When Andy goes to his room to get Molly, he lowers the side of her crib in order to get her out, picks her up, and walks out of the room. In the next shot of his room, the crib side is back up.
Continuity mistake: While Andy's falling asleep, when Potato Head and Rex pop out of the Eggman Mover's box it has "Andy's toys" written on one side and the adjacent side is solid - no openings, but when Woody opens this box in the moving truck, there are now open handle cutouts on the two adjacent sides to where "Andy's toys" is written.
Continuity mistake: In Sid's room, there's a lightbulb hanging over the table (which he turns on when he switches the doll's and pterodactyl's heads), and its electrical cord that hangs beside the lava lamp (filled with toy heads) vanishes and reappears a few times during the scenes there.
Other mistake: There are six various bolts, locks, and latches on Sid's door above and below the doorknob, and some are in their locked positions when the door either opens or closes. For example, after Sid replaces the doll head with the pterodactyl head and calls Hannah, when the door's open we can see the dead bolt and slide latch are both slid out in their locked positions and yet Sid's able to open and shut the door, which is quite impossible.
Other mistake: While Sid's toys are working with Woody to get Scud out of the house, just as Hand-in-the-Box is holding the doorknob we can see the screw mounted on the latch's hasp below the loop - which really doesn't make any sense, but as Hand opens the door the screw has suddenly vanished from the hasp and is now properly mounted on the doorway's loop plate, where it's meant to be. If the screw were really mounted through the hasp, the door could not be opened.
Continuity mistake: There's an electrical outlet on the wall below the window (aligned with the window shade's loop) in Sid's room near the Megadork poster, but when Sid throws Woody to the floor and raises the shade (before he scorches Woody's forehead with the magnifying glass), that outlet has vanished.
Continuity mistake: After Woody tosses the string lights to Andy's toys at the window Mr. Potato Head hangs onto the end of it, but in the shot from behind Andy's toys when Woody's shaking Buzz's arm and imitating his voice, we see the outside of Sid's window and the string lights have vanished, then they reappear.