I recently read a story that would never work without an omniscient narrator. The story is by Mohammed Hanif, and it's called Butt and Bhatti. It was originally published in Granta magazine and reprinted in the 2011 edition of The Best American Nonrequrired Reading. It's also a stand-alone excerpt from Hanif's novel, Our Lady of Alice Bhatti. And it takes place in Karachi, Pakistan, where "Butt" is a perfectly reasonable last name that has none of the connotations it would get if an American character were named "Mr. Butt." (My initially negative reaction to a "Mr. Butt" character is just one of the unfortunate ways cultures can clash.)
In this excerpt, Teddy Butt has brought a gun to a hospital because he's in love with one of the nurses (Alice Bhatti) and he's convinced bringing the gun will help him win her love somehow. (He's not an entirely stable man.)
"What do you want, Mr. Butt?" Alice Bhatti tries to hide her fear behind a formal form of address. She has learned all the wrong things from Senior Sister Hina Alvi.
"You live in my heart," Teddy Butt wants to say but only jabs the air with his Mauser, five times. In her limited experience with guns and madmen, Sister Alice Bhatti knows that when men are unable to talk you are in real trouble. She looks at him expectantly as if she has understood what his Mauser has just said, likes it and now wants to hear more.
I think the secret to how well this excerpt flows, despite leaping back and forth between POVs, is that the text tells the reader, flat out, what thoughts belong to what characters. Switching POVs is no time to worry about that "show, don't tell" rule. You have to hit the reader over the head:
Alice Bhatti tries to hide her fear...
"...my heart," Teddy Butt wants to say...
In her limited experience...
(HER experience, and since there's only one woman present, it's got to be Alice)
So remember, there's no room to get cute when you're dealing with the omniscient POV. Tell the readers directly who is thinking what, who is feeling what, who is seeing what. Otherwise, the story will confuse readers on such a fundamental level that they won't be able to follow it, much less enjoy it.