Deliberate mistake: The top of the Tipton Hotel is animated. You can tell because in the opening of any episode showing the top of the hotel, there should be 3 visible peaks. You can see 2 peaks and if you look where the middle peak should be, you can see through the top of the hotel to the sky on the other side.
Continuity mistake: Zack puts Cody's whistle in their mate's pudding, but when Cody says, "You got pudding on my whistle" and the mate says, "And you got whistle on my pudding," the whistle is gone from the pudding, between shots. Then, a few shots later, we see that Cody is holding the pudding drenched whistle. (00:08:00)