Continuity mistake: At the beginning, when Andy gives Woody to Bonnie, their interaction and how Bonnie reacts is quite different than the previous film. At the end of Toy Story 3, when Bonnie sees Woody still inside the box she says "My cowboy!," then Andy describes in detail why Woody is so special and gently hands the toy over to Bonnie, and she quietly hugs Woody. In this movie Andy is holding Woody when Bonnie says, "My cowboy!," then Andy gives the toy to Bonnie and she hugs Woody. (00:06:20)
Factual error: In the antique shop, Woody is at a point where he's at the center of a tug-o-war between two sides, with the "bad toys" pulling on his draw string for his voice box. The voice box can still be heard spouting its lines, despite the fact that the tension on the string is never released allowing it to draw the string back in, which is what makes the sound. It can't make it's sounds with the string continually out in the pulled position.
Continuity mistake: When Buzz is first put on the prize board at the carnival game, Ducky and Bunny are hanging further down and Ducky is pretty much level with Buzz. Later on, they are hanging higher up and Ducky struggles to reach Buzz when trying to kick him. (00:34:22 - 00:43:00)
Continuity mistake: When Bonnie is running toward her parents while shouting, "Mom, Dad, look what I made," Bonnie's holding her backpack's top handle with the front of the backpack facing her. Then it cuts to Bonnie running into her mother's arms, and now the backpack is positioned the opposite way with both shoulder straps facing Bonnie, as she is still gripping that backpack's top handle in her hand. (00:14:05)
Continuity mistake: Throughout this movie we see Buzz and Woody both use their voice boxes. However the lines that are issued from them are completely different to the rest of the franchise. There are 1 or 2 (There's a snake in my boot is a good example) from previous films, but given the limited capabilities from the "late 50's" as acknowledged by Woody in the store, there should only be the few lines from the first film.