Short review: I enjoyed it, but I think it's far and away the least of the four. As glad as I was that Will & Elizabeth weren't brought back (their story is done and should remain so), I was pretty worried about what it would be like with Captain Jack in the lead, as opposed to an absurd, trickster/anti-hero third lead. It turned out better than I imagined, though, because we're not given a new emotional investment in Captain Jack; he doesn't suddenly become a sincere figure with great pathos. You do feel the absence of characters like Will and Elizabeth, though, anchors who can support or ground the wildness of the rest of the proceedings. The missionary and the mermaid are essentially Will & Elizabeth stand-ins, but really, they're such afterthoughts as characters, we don't care about them one whit. And they lack the chemistry and charm that Orlando Bloom and Keira Knightley had together. As fun as Captain Jack Sparrow is, as deliciously pirate-y as Captain Barbossa is, who do we care about in this movie? Johnny Depp and Penelope Cruz were fun together here - I've seen and heard some complaints that the nature of their relationship was confusing because it seemed to be always changing. Yes, that's sort of the point; you're never sure where they stand - neither are they. The biggest problem with this movie might be that it doesn't have a particularly strong villainous presence; Ian McShane's Blackbeard isn't a memorable villain, and, although he's not a true villain by this point in the series, I didn't love the handling of Barbossa. He felt so disconnected from things for so much of the movie. Now, of course he had a very significant connection to Blackbeard, but that comes in later. Pirates of the Caribbean: On Stranger Tides is not remarkable, in either the positive or negative. It's merely okay.
I said short review, didn't I? Ah well.