"For third-person to work, if you're describing what people are thinking/feeling then it has to be from a limited set of characters or not at all."

That's far too broad a statement. This matter depends on the "contract" the writer has made with the reader: if by the end of the exposition, the author has told you that she is only going to get into the head of the protagonist, then it is certainly weak writing on her part to jump into the head of a passerby on page 89; if, however, she has made it clear from the outset that she's going to be inhabiting the heads of (potentially) all of her characters, there is no particular criticism that can be made on that count other than that you don't like it, or that it wasn't the right choice for the novel in question. There is certainly weighty precedent for the busybody omniscient narrator - Fielding, for example, in Tom Jones, delves into the thoughts and feelings of almost every character that enters the story. And to go back into the era preceding the novel, Shakespeare gives the otherwise most-insignificant spear-carrier asides that reveal what's going on in his head ...