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.
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 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.
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 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.
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.
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: 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: The blue blanket in Molly's crib repeatedly vanishes and reappears within the same scenes, such as when the batteries are put back into the baby monitor Woody shouts for everyone to return to their positions, in the overhead shot of the room the blanket's gone, but is soon back in its place.
Continuity mistake: Before Woody uses the remote control to have RC push Buzz off the desk, there are red, yellow, and blue pushpins in an empty area of the bulletin board, but after RC hits the bulletin board, in the closeup of the pushpins falling off those colors have changed to green, red, and yellow, with the green pushpin remaining in the empty space, but when the bulletin board starts to fall over that green pushpin is gone and it's back to the red, yellow, and blue pushpins.
Continuity mistake: In Andy's room, the general ("generil") store box under the crib near the closet door has a cow illustration on its right side, but in the next few shots there's a drawing of two windows on that side of the box, and then it keeps switching between the cow and two windows in following shots.
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: 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.