Revealing mistake: The flags on Tipton hotel you see almost every episode never move; they're animated.
Revealing 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.
Visible crew/equipment: Sometimes when they're at the pool and someone has sunglasses on, you can see the reflection of a studio light.
Other mistake: The characters that are supposed to be native to Boston, Massachusetts, i.e. Maddie, Maddie's parents and Red Sox fans, don't ever actually speak with the iconic Boston accent.
Revealing mistake: London's phone screen is visible, and it is shown that it is not a real digital phone.
Visible crew/equipment: In the episode "Hotel Inspector", when the man with glasses comes in, you can see a light on his glasses that looks like a studio light. (00:18:30)
Visible crew/equipment: In the episode "Hotel Inspector," when London comes to tell Maddie about something, she says, "Dogs playing poker," and you can see studio lights on her sunglasses.
Continuity mistake: Zack and Cody's mom takes away the rats to Zack and Cody's bedroom. She goes behind the sofa, but in the next shot of the door, she's not to be seen anymore.
Grounded on the 23rd Floor - S1-E5
Visible crew/equipment: At the beginning of the episode 1x05 "Grounded on the 23rd Floor", when we hear the classic song, if you look closely at the door windows, you can see a studio light. (00:00:10)
Grounded on the 23rd Floor - S1-E5
Continuity mistake: Zack and Cody skate in the lobby and push a guy with a golf bag. It falls and spills the golf clubs onto the floor. A big guy trips on it and falls over Mr. Moseby, and after that the golf bag is not seen. (00:00:35)
Grounded on the 23rd Floor - S1-E5
Visible crew/equipment: At the beginning of the episode 1:05 "Grounded on the 23rd Floor", when the big guy is falling over Mr. Moseby, you can see studio lights in his eyes when he yells "mamma". (00:00:40)
Grounded on the 23rd Floor - S1-E5
Visible crew/equipment: At the beginning of the episode 1x05 "Grounded on the 23rd Floor" after the big guy falls over Mr. Moseby and everybody looks at them, look at Zack and Cody's helmets: you can see a studio light. (00:00:50)
Grounded on the 23rd Floor - S1-E5
Visible crew/equipment: When Maddie gives Zack and Cody the "US People" magazine, you can see a studio light on it. (00:07:00)
Grounded on the 23rd Floor - S1-E5
Continuity mistake: In the episode 1x05 "Grounded on the 23rd Floor", Zack and Cody give all the candy for a camera. They put it all on the table, but when they get the camera, all the candy is gone. (00:08:00)
Grounded on the 23rd Floor - S1-E5
Continuity mistake: In the episode 1:05 "Grounded on the 23rd Floor", when Cody falls from the porthole, two glasses are on the floor, but later when they run after the papparazi, the glasses are gone. (00:15:45 - 00:18:25)
Grounded on the 23rd Floor - S1-E5
Continuity mistake: When Carey opens the suite door to find Moseby with the hotel bill, then when the room service arrives and in the following shots, the twins' backpacks' straps are on, then off, then on, then off and so forth.
Grounded on the 23rd Floor - S1-E5
Visible crew/equipment: When Maddie and the boys are crawling through the air vent, a boom mic can be seen on the right side of the screen.
Grounded on the 23rd Floor - S1-E5
Continuity mistake: When Carey is confronting the boys, she places her hand on her left hip twice.
The Prince & The Plunger - S1-E6
Visible crew/equipment: Zack and Cody go to Arwin the first time and get donuts, but when Arwin says it's going to be a steak next time you can see the studio lights reflected in his glasses. (00:09:15)
Visible crew/equipment: At the beginning, you can see studio lights reflected on Zack's guitar during the song "Schools Out". (00:00:55)
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.