Visible crew/equipment: At the beginning, you can see studio lights reflected on Zack's guitar during the song "Schools Out". (00:00:55)
Visible crew/equipment: When Cody tells his mother how much he hated Zack, you can see the reflection of a studio light on the chair he is sitting on. (00:08:45)
Visible crew/equipment: In the episode 1.09 "Band in Boston", Arwin comes in with his "Saxoblower." He puts on sunglasses and you can easily see studio lights reflected in them. (00:12:55)
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)
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.
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.
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 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.