Paul, both the character and the film itself, is kind of a one-trick pony. Paul is an alien who crash-lands on Earth in the 40s and escapes from the government in present day into the hands of two British nerds (Simon Pegg and Nick Frost), in from England for Comic-Con and a road trip to all of the extra-terrestrial-related sites in the American Southwest.
It's a pretty nice little movie until Pegg and Frost actually meet Paul, who essentially just acts contrary to most on-screen aliens have in the cinematic past, which would be refreshing if it didn't mean simply swearing, getting naked, and getting high. That still might sound satisfying enough, but it honestly just gets old really quickly. Aside from a few random inserted jokes, like a flashback to 1980 that has Paul giving Steven Spielberg some advice on what E.T. should be like, Paul doesn't really offer up much that is worth your while. And aside from a handful of top-notch Star Wars references, Pegg and Frost don't really do too much either. There are some great supporting performances from Jason Bateman, Joe Lo Truglio, and Bill Hader, as well as an amazing cameo by Jeffrey Tambor as an asshole of a sci-fi novelist doing a signing at Comic-Con... "Did you buy a book? Well, then get the fuck out of here."
Paul really isn't a bad movie; it's enjoyable enough, but it's just kind of bland. It's not that the jokes fail, so much as the jokes are not even there to begin with, and there isn't enough plot, character depth, or just general originality in the film for it to be lacking in humor.