When "demo" Buzz escapes from under Rex and Hamm, and is running to get away from the toys, he opens his left arm to call out to Star Command, saying he is being held captive by his own prisoners. When Buzz thought he was the real Buzz Lightyear (in Toy Story), he always pressed the red button on the right side of his chest to call for Star Command.
When Lotso removes Mrs. Potato Head's mouth, she is unable to use it. This might contradict many other instances in which the Potato Heads are able to use their body parts when not connected to their body, but it seems that Lotso is also squeezing Mrs. Potato Head's lips together to impede her speech.
The toys never let people know they are alive, but several escape attempts, patrols by Lotso's gang and other things are recorded by the security cameras at the day care center. It is possible to alter images seen on security cameras, and conceivable that one or more of the toys in Lotso's gang would know how.
When the toys are taken to the curb to be picked up by the garbage truck, there are three garbage bags. When the garbage man picks up the bags, there are only two. Andy puts the toys in the 3rd bag and when woody splits open the 2 remaining bags they are full of garbage so are obviously not the bag with the toys in. The toys must take the 3rd bag with them during the escape.
During the incinerator scene Slinky Dog is first pulled to the ceiling, realizing its because of a magnet the other toys grab metal objects to get pulled up and escape the grinder. On the other side of the grinder the toys release the metal objects and fall back to the conveyor belt, inexplicably Slinky is there with them and the magnet seems to no longer affect him.
Andy is giving his toys to Bonnie. He shows her the three aliens from Pizza Planet. All three are facing her but when Andy puts them down in front of her, they suddenly change direction to be facing Andy.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
When Andy is introducing his toys to Bonnie, he introduces Jessie. In Toy Story 2 when Jessie came to live with Andy he gave her the name "Bazooka Jane". However, he gives her that name before using her pull string. The message "My name is Jessie, pleased to meet you" is featured on the toy and so Andy had a few years to pull the string and learn her real name. Furthermore, it could've simply been a nickname that he gave her, similar to how he calls Mr. Potato Head "One Eyed Bart" and Hamm "Evil Dr. Porkchop".
Lotso pleads for help in the compactor scene. When we see his arm rise from the trash, the platform is moving towards the compactor. The camera switches back to Woody who is trying to make a decision. When we switch back to Lotso, the platform appears to be moving away from where the compactor is, backwards. This effect of an apparent change in direction is caused by the fact that the magnet strip above is moving faster than the garbage platform below,as can be seen in previous scenes.