Continuity mistake: When Zack and Cody finally come to the stage, Cody has a sock over his sweater and it's still there when they start singing. But in an instant the sock is gone. Cody could not have taken it off, because he was too busy playing piano.
Christmas at the Tipton - S1-E21
Continuity mistake: Season 1, episode 21 'Christmas at the Tipton': When Arwin leaves to fire up "Old Betsy", he trips over the couch and when he breaks the table its broken pieces differ between shots.
Visible crew/equipment: Episode 1x09 "Band in Boston", the reflection of studio lights are visible on the drums almost every time they are seen during this episode.
Continuity mistake: Season 1, episode 22, 'Kisses and Basketball': The twins' mom is sitting in the back and she has her hands down. When Arwin says "Let's kick some" it cuts to their mom and she has her hand on her neck, it then cuts back to the basketball team and she has her hands down by her lap again.
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.
Visible crew/equipment: When Zack, Cody, Tapeworm and Max are singing "School's Out" on stage, you can see the shadow of the camera crane.
Continuity mistake: Season 1, episode 16 'Big Hair & Baseball': In the lobby, when Cody comes to the defense of Moseby, Zack is holding two ice cream cones and as he continues eating, more of the ice cream appears between shots.
Continuity mistake: Season 1, episode 19 'Ghost of 613': When London finds her gold purse in suite 613, she places it on her left arm just as the noise at the door scares her, but when Cody tries to jump into her arms the purse is on her right arm.
Grounded on the 23rd Floor - S1-E5
Continuity mistake: When Carey is confronting the boys, she places her hand on her left hip twice.
Visible crew/equipment: Season 1, episode 24 'Crushed': When Esteban holds the tray with the dogs' food, the studio's numerous overhead set lights are reflected on the surface of the large, silver, dome lid.
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.
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.
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.
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.