I remember there was a lot of hype when At World's End came out (though it may have helped that the media took advantage of the fact that it was one of three third movies to come that month, along with Shrek the Third and the equally if not even more critically panned Spider Man 3). The trailers promised us a lot: plenty of action, epic swordfights, and a few new characters. What we got was a bit of a mess. I've cited various issues as the reason why this movie failed, but I think I've finally figured out the problem. Quite simply, while it tried to go in some new directions, it may have gone a little bit too far.
The reason I think The Curse of the Black Pearl worked was because it was, at its core, simply a fun and straight forward adventure film. We had some complex characters and a bit of drama here and there but it was always balanced just right. The film never took itself too seriously but also never took itself too lightly.
Jack Sparrow was a lot of fun but his comedic antics were balanced with the much straighter characters of Will and Elizabeth. Say what you will about Dead Man's Chest but it did retain at least some of that atmosphere. There was a bit of humor but it never took itself too seriously or lightly.
The problem with At World's End was in its effort to bring in new elements it went completely overboard (no pun intended) to the point where it seems completely out of place in the franchise. Instead of being a fun nautical adventure with some lovable characters, it tried to be some kind of epic drama, which really didn't mix well with the elements that were lifted from the previous films.
While the new characters were okay the plot itself got insanely convoluted and maybe had a bit too much going on, not to mention I was never particularly satisfied with the ways they killed off certain characters from the previous films (Norrington letting himself get stabbed when he could have easily climbed on that rope and gotten away coming to mind), and then we have this whole thing with all the "Pirate Lords" acting like piracy is some kind of international organization and they act like it's going to vanish forever (all it'd take to bring it back is one person getting onto someone else's boat and committing a robbery).
So to put it quite simply, the major problem with At World's End is that it really misses what made the other films enjoyable. I'm even one of the few who actually enjoyed On Stranger Tides, and what I'd say made that film work was that it went in a bunch of whole new directions while still understanding why people liked The Curse of the Black Pearl. We got a whole new group of characters, aside from Jack and few supporting roles, but it doesn't try to be a convoluted Lawrence of Arabia-style epic. Indeed, some movies can work really well as epics, but there's a big difference between making a movie that lends itself to being an epic and trying to convert a fun and straight forward pirate adventure into a genre where it doesn't belong.