Continuity mistake: In the episode "Commerical Break," they start to film the commerical for the first time without London and with Mr. Mosby. London gets upset and sits down on a couch where they are shooting the commerical. She and the couch leave the shot for a second, and London is gone when they show the couch again.
Continuity mistake: In "Boston Holiday", Zack is talking to Mr. Moseby in the hallway. In a wide shot, behind Zack, you can see that the elevator door is closed. But when it cuts to a close-up, the door is suddenly open. There wasn't enough time between shots for the door to open.
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.
Other mistake: In the episode "Its a Mad, Mad, Mad Hotel", when Esteban has his dream of becoming rich and London becoming his "Bell Girl", he calls the hotel "Hotel Esteban, but London's uniform still has a "T." When it cuts there is an "E" on the front desk.