Revealing mistake: When Arwin gets both the seven and the ten bowling pins causing Team Tipton to win, if you look very closely at the close up of when he hits them, you can see that someone is controlling the pin with something to make it hit the other one, because right before he hits it, you can see the pin jerk a little before anything touches it. Pretty obvious.
Continuity mistake: When Zack trips on the slick floor, his red backpack ends up behind Cody, but in shots facing the kitchen the backpack is across the room, near the kitchen cart.
French 101 - S2-E2
Continuity mistake: In their attempt to make Esteban feel better, when London stands at the doorway shouting at Maddie outside, the colorful shopping bags on London's arm change their order in the close-up.
Continuity mistake: Season 1, episode 9 'Band in Boston': When Cody and Zack are arguing over Zack's look (vs Cody's lyrics), the black cord (with whistle) goes from under Cody's shirt collar, to over, back to under, between shots.
Revealing mistake: This is very obvious. When Zack comes back with the bike and gives it to Cody, and it breaks apart, you can definitely see at one point the string/wire that holds it together.
Nurse Zack - S2-E29
Visible crew/equipment: After Patrick dumps the cake on Moseby, he wipes some away from his eyes. At the start of the next shot, when a crewmember's finger moves across the bottom of the screen it cues Patrick, who makes eye contact with the finger, to exclaim his line, "You did this on purpose!"
Visible crew/equipment: Season 1, episode 9 'Band in Boston': After Zack dips Cody's whistle in the pudding, when Zack rips up Cody's music have a look at the floor where you will see the actors' tape marks.
Plot hole: The whole episode is based on false facts. Cody was getting an A in woodwork and Zack was failing in all his classes the previous year at school (according to their report cards in Ep "Smarter and Smarter"). So Cody knows a lot more about woodwork than Zack and should be able to make a clock, never mind a birdhouse, and Zack should not be able to make a clock.
Answer: Keep in mind, Muriel wasn't very popular. So the writers/directors must have thought it'd be a good idea to let go of the character. No one seems to be complaining.