Hyperion starts in third-person. However, much like the plot itself, the P.O.V.s shift back and forth more than (insert political candidate here)'s views on (insert sensitive political issue here).
The majority of the book is told in a third-person limited point-of-view, most of the time following around the Hegemony Consul. Even though we get more glimpses of his inner thoughts than we do any of the other characters, we never learn until the very end that he's the Ouster spy. (That's some tricky storytelling.)
But between his perspective we get the characters' tales, and not every story is told in its teller's voice. The Priest's Tale is told epistolary style, through a missionary's journals. The Detective's Tale and the Poet's Tale are first person, which makes the stories sound intimate. The third-person stories (the ones that are mostly about someone other than the teller) create more distance between you and the characters, although the stories aren't any less compelling.
Like having so many different settings, the constant shifting adds to the general disconcerting feeling of the story. Just like you would if you were traveling to a new planet—especially one as spine-tinglingly frightening as Hyperion—you just don't know what to expect.