Early in the movie, in the scene where Woody is rubbing the belly of Andy's dog while on its back. Watch the left side of the dog's front legs as he's squirming. You will see an obnoxious red glow dance up and down the leg. This appears to be the most noticeable and long-lived rendering problem in the movie.
I don't know if this is true or not, but even if it is, it's not a slip-up. Didn't you know that Buzz also has a red laser? (not a real one). I don't know why Buzz would be pretending to kill the dog, but he might just be mucking around.
Oops. I forgot to mention that this slip-up required seeing the original movie, not the video/DVD release. Unlike most movie transfers, which are "panned and scanned" from film to video, Pixar re-renders the movie from their original data to make a totally clean version for 4:3 home video systems. They would have undoubtedly taken advantage of this opportunity to fix rendering problems such as this "puppy" problem.
The problem WAS there in the original release. I know, because I was fortunate enough to get to sit in while director John Lassiter and others reviewed the movie just days before its release. Laser pointers highlighted each problem that had not been fixed (before the film prints were made), the worst of which (to my eyes) was the "puppy" problem.
And no, this wasn't Buzz's laser -- read the description again.
After watching the home video release of this section (which is about 07:50 into the movie), I noticed that the problem is still there, but much less noticeable. It lasts much shorter than before, and the flashes are more white than red. Look at the left side of the dog's front leg when Woody says "I'll see you Sunday night."
Maybe this got cleaned up some before the video release, or maybe NTSC just hides that much stuff. The latter is certainly true, since another egg that I was going to share about TS2 is totally lost in the home video version: when the toys are going to cross the busy street and the car kicks up the soda can, on the big-screen version you can discern words to the effect of "Eggman Soda" on the can as it hits the ground. Like the "Eggman Movers" truck in TS, this is a nod towards art director Ralph Eggelston.