In Susan Sontag's awesome essay "Notes on Camp", she makes the suggestion that camp is born when the execution of something fails to meet its ambitions. If you choose to agree with this, Sleuth is an absolutely perfect example of it.
Consider first its source material. The original Sleuth, which in itself was an adaptation of a play, was highly literate and a little bit stuffy but incredibly clever nonetheless. This makes many of the same bids at intelligence while excising that stuffiness, but when it deviates from the original movie, it fails horrifically. The last twenty minutes, for instance, are new: a psychosexual pissing contest that tries to be mentally probing but just ends up laughable and vaguely smutty instead. It's like Basic Instinct's gay leftovers. And just like Basic Instinct, this is trash masquerading as brilliance, living under the impression that being dialogue-driven automatically lends it intellectual credibility. The result is something you feel a little embarrassed for as you watch.
But the movie isn't unwatchable - it's just very different and enjoyable on a separate level from the original Sleuth. The set design is neat, opting for a sort of technological utopia versus the eerie toyhouse of the first movie. There's something very interesting about the directorial decisions Kenneth Branagh makes: he rarely films the actors face-on. There are a multitude of above-the-head shots, or shots via surveillance cameras, or shots interlaced by blinds. Michael Caine and Jude Law rarely appear in the frame together. I wasn't really sure why he was playing around with the cinematography so much, until I read a review that suggested he was trying to meta the whole movie. Remind us that it was a big theatrical mess. I totally understand that, because there are a few bits of dialogue that sort of take the piss out of the whole thing.
As for the participants themselves...Michael Caine, playing the role he played against in the first movie, is obviously having a good time. There's a lot for him to do here: he gets to be devious, arrogant, bemused, terrified, lovelorn, gayyy, murderous. It's an overly theatrical dream! Jude Law can't really match stride, and I get the feeling he was taking the whole thing more seriously, but damn if he isn't bangin'. His hair is gross-looking and he weighs about 90 pounds soaking wet, but I would nail that. He kind of fits in with the lurid trampiness of the whole affair. So I forgive him his diminished understanding.
Anyway, Sleuth is a really big but entirely entertaining mess. I understand why it didn't get much of a theatrical run, because there's no audience for this kind of movie. Still, I imagine it'll get rediscovered ten years from now by people who are looking for ignored "clash of the movie stars!!!" flicks that are full of camp sensibilities. Sleuth does a great job filling those shoes.