A few that come to mind are:
Aladdin (the minimalist genie, it shouldn't be minimalistic)
Next to Normal (the eyes & music notes, it's an amazing show but they have nothing to do with it)
Violet (the bus with her face, anyone could whip that up in five minutes on Illustrator)
Hairspray (Tracy's face, it's just horrible)
It Shoulda Been You (the wedding cake, it looks too sketched)
Newsies (Jack jumping, I just don't get it)
Some amazing logos I can think of are:
Hamilton (the star with LMM/Hamilton on the top)
Les Mis (the girl)
Matilda (her pose)
Tarzan (him as the Z)
Wicked (I don't think I need to specify)
Rent (I LOVE the papers)