The burn mark on Woody's forehead disappears once he is at Andy's new house celebrating Christmas.
When Andy puts Woody and Buzz on the desk, there is no Magic 8 Ball - but a second later the Magic 8 Ball appears right next to Woody.
When the RC car runs out of batteries, Buzz drops the remote control. That remote disappears from the street when Woody lights the rocket.
The lever that lowers the ramp on the moving truck changes from black to red.
Before Woody asks Buzz to free him from the tool box and milk crate, the clock on Sid's wall jumps to 6:25. After Woody closes the door to block Scud and he sees the mutant toys, the clock jumps from 6:25 to 3:10. After planning the rescue of Buzz from the rocket, and Legs and Ducky remove the air vent cover and crawl through the air vent ducts, the clock jumps from 3:10 to 10:00.
When Legs and Ducky remove the porch light fixture to ring the doorbell for the escape, they pull the fixture up through the hole in the ceiling. They are also able to lower it back through afterward. One would be unable to do that with a real fixture of that sort, as housing would be bigger than the hole so it could be attached to it.
At the Dinoco gas station Woody plays dead. He somehow has managed to get past the truck's front left wheel. He would have been crushed before the back tires reached him.
During the birthday party, the toys use the wrong parts of the baby monitor to communicate. Sarge is using the receiver and Woody is using the transmitter; it should be the other way around.
In Sid's room, there's a lava lamp with a toy head floating in it. There would be no way for Sid to get that head into the lamp.
When Woody or Buzz look through the binoculars (Lenny), the view is shown to be the typical double image even though they can only look through one opening. The image should be like looking through a telescope.
Even though Buzz believes he is a real space ranger and not a toy, he still freezes when people are around like the other toys do.
Every time he freezes it is because Woody says "Freeze" and being a space ranger with years of training in covert missions, freeze means to be still.
Rex combines anatomical elements of Tyrannosaurus Rex, Giganotosaurus, and other dinosaurs. He's a generic caricature for toy marketing, not a scientific exhibit.
Sarge's binoculars are made of opaque plastic. He shouldn't have been able to see through them, but this movie's toy logic is arbitrary.
When Woody is a regular toy, his mouth alternates between closed and smiling to partially open. However, this is not exactly a goof as Woody simply freezes his face.
Molly is in her car seat in front of the van. While airbags are hazardous for children under the age of 12, passenger-side air bags were still fairly uncommon in 1995, making it possible this van wasn't equipped with one.
Buzz's wings should have been caught on the car track loop when he demonstrates how he flies.
Near the beginning, when Woody is on the bed, a rendering
error occurs when, as he gets up, his left hand passes through his face.
When Sid puts the Alien on Scud's nose, look at Scud's chest as he breathes. His chest seems to be passing through his legs. This is a rendering error.
When Mr. Potato Head does the butt kissing joke at the staff meeting, a rendering error occurs when his hands pass through his mouth.
When Sid is lying in bed, the color fades off his face.
Throughout the film, an important plot point in the film is that Andy's family is moving within days. This fact is mentioned when Woody tells the toys that there is one week left before moving day and there are repeated mentions of the moving in progress throughout the film which takes place over at least a few days to a week. Yet, during "Strange Things", Woody sees Buzz becoming the dominant toy in Andy's room, Andy's mom has gone through the trouble of changing the room from cowboy-themed to spaceman-themed. Generally, there would be no point in such a dramatic decoration change if the family is planning to move out of the home within days of Andy getting Buzz for his birthday.
Woody is stuck under the milk crate in Sid's room next to a United States Army manual called "TM 31-250: Improvised Interrogations Handbook". Catalog number TM 31-250 is actually the "Improvised Munitions Handbook".
The Davis' minivan has lap belts only. Full seat belts are required by federal law as of the year of the film's release. Full seat belts were mandated by NHTSA for the front seat in the mid 70s; and then by 1989 became mandatory for all seats other than just in the front seat.
The balloons that are seen in the Davis' living room have four candles on them. This makes it seem that Andy is celebrating his fourth birthday. However, Andy is celebrating his sixth birthday.
When Buzz notices that his cardboard spaceship is damaged and says "Blast! This will take weeks to repair!", his lip movements don't fully match up. Presumably, he was originally meant to say "Damn!" before it was changed to "Blast!"
When Woody tells Buzz to snap out of it, he removes Buzz's helmet. After he removes the helmet, Buzz is still laughing but without sound until he is slapped by Woody with his own broken arm.
When Woody lifts the Mega Gulp cup, he is heard coughing, but his mouth stays closed.
When RC is dropped into the moving van, Rex is heard saying "Take cover!", but his mouth does not move.
When Buzz and Woody first meet, Buzz points his laser at Woody after getting startled by him but when the camera changes to Buzz's arm none of his fingers are pressing on the button that emits the laser.
At the gas station, Woody and Buzz get on the Pizza Planet truck, which has amber rear side markers. However, US-Spec requires vehicles have red rear side markers; amber rear side markers are Euro-Spec.
Given that Andy's mom states that he is old enough to pump the gas and drive when he is 16, it is implied that the Davis family lives in the United States. However, their car's license plate reads "MINIVAN" instead of a state. The best view of the license plate is when Woody climbs onto the car's trunk and holds the rear wiper down.
Throughout most of the film, Buzz actually believes that he is a real space ranger and not just a toy. However, when Andy's toys first get introduced to him, Rex asks him what a certain button on his chest does, which he demonstrates by pressing it showing that it plays a fanfare and saying, "Buzz Lightyear to the rescue!" If he knew the button did that, one would assume he would know he was a toy. Not only that, but before Buzz meets the toys, he tries to communicate with Star Command by pressing that same button, and nothing happens.
All the toys are believed to have a soul within them, which makes them come alive. RC is seen falling behind because of low batteries. Since RC is alive, it would have no use for batteries.
Trying to escape from Sid's room, Woody gets his pullstring ring caught and pulled, playing one of his catchphrases through his voicebox, which gives him away to Scud. However, when he freaks out Sid in the backyard, he seems to have control over the voicebox when he's not "alive".
No one at Pizza Planet notices that Sid has tampered with the Whack-an-Alien game. Sid is also not ejected from the premises for tampering with that game.
Sid's mother neither scolds him for playing with matches nor committing arson at any point in the film.
When Buzz and Woody are trying to get back into the moving van, Woody opens the boxes of Andy's toys in search of R.C. All the toys react to having the box opened by shielding their eyes and commenting on it. However there was no guarantee that it was a toy opening the box and therefore they could have just revealed their ability to talk/move to either a removal man or any member of Andy's family.
When Sarge looks through his binoculars for the first time, they are upside down.
When the 18-wheeler parks, Buzz and Woody argue for a long time, yet the driver never gets out of the vehicle.
When Sid's mutant toys first appear and take Janie's torso to repair her, at the second close up shot when they take her torso, the dress and shoes look more like Mary Antoinette's little sister, seen later in Hannah's room.
The toys use a skipping rope to allow the army men to make their way from the landing to the ground floor. If they know that the rope can reach that far, it seems odd that they did not consider using it to rescue Buzz after he was knocked out of the window.