Here is what Sol Stein says in Stein on Writing.
'In general, I advise the less-experienced writer not to mix points of view within the same scene, chapter, or even the same novel. It is unsettling to the reader. If you mix points of view, the author’s authority seems to dissolve. The writer seems arbitrary rather than controlled. Sticking to a point of view intensifies the experience of a story. A wavering or uncertain point of view will diminish the experience for the reader.
Interesting. Thanks for pointing that out. I was never a fan of Stein's advice and I'll continue to steer clear.
I think this is terrible, terrible advice. If a writer doesn't have a good control of point of view, the writer should improve this aspect. It's going to affect the prose regardless of the amount of povs in a book.
Yeah, a wavering POV sucks, but it's going to suck no matter what. I've read stories with poor POV control, and it slips even if it's in first person or limited third. If the POV is poor, the narration and the prose suffer, so it's better to get that fixed, and choosing one single POV is not going to fix that, unlike what Stein suggests.
I also disagree that you will have a stronger "author's authority" with a single pov. WTF is even author's authority? Is is the author's voice? I don't really like it when I see the author's voice creeping through the narrator, with some exceptions. Austen, for example, has a delightful sarcastic and snarky voice that's always a pleasure to read. She achieves it through an omniscient narrator who actually peers into different POVs. In fact, her going in and out of heads allows us to get the super snarky narrator's voice as an entity separated from the character's thoughts. Not everyone's Austen, sure, but still, I don't think people want a narrator's voice in contemporary fiction. Also, sometimes people think that the character's voice is the author's voice, and it's easier to make the distinction in a book with different voices. Not that everyone can write in different voices, though, and in this case I understand it's easier to write in one single POV (so perhaps I agree with Stein a little, but for very different reasons).
I also find that multiple POVs can create suspense, and work really well for a climax, for example, if you have something like:
Character A's pov chapter ending in cliffhanger.
Character B pov cliffhanger.
Character C pov cliffhanger.
It can be a lot more interesting and intense than if you solved character A's issue right away. It can be sometimes infuriating for readers, but I think if povs are interesting it works. I hate it when I shift from an interesting POV in a cliffhanger to a boring POV in which nothing happens. I also dislike it when authors add the same events from different POVs. OK, sometimes it's cool to see how they react differently, but you don't need to narrate the scene twice.
So sure, there are ways in which multiple POVs can be terrible, like with anything.