It's a shame this movie is so boring because while you're watching it, you feel like it shouldn't be. For starters, this movie is really neat to look at. The director Stephen Norrington is a great visual stylist. The action sequences--on a purely visual level--are exciting and dynamic.
So what went wrong? First off, I would say the lead performance by Sean Connery is a definite liability. It is the very definition of a phoned in performance. He looks bored. For example, in his introductory action sequence, pretty much all of his friends in Africa get killed but he just goes on making quips like it's no big deal. Beyond Connery, Peta Wilson is the only actor who seems to be having any fun.
The other big problem is that the script is so lame-brained. Like I said, the action sequences are visually exciting, but because the stakes are never very clear going into them, they end up feeling like a lot of sound and fury signifying nothing. For example, in their first encounter with The Phantom in the library at Dorian's house, they fight with the Phantom's henchmen and he escapes. But then later we learn that [SPOILER ALERT] M is the Phantom and that M is trying to steal their abilities. So why the hell was the Phantom trying to kill them in the library?! It's a neat looking action scene, but ultimately pointless. Similarly, the mid-point action sequence in the Venice canals is wonderful to look at, but the physics of it make absolutely no sense. Apparently, the buildings are falling like dominoes and if they destroy a building in the middle of the city, they can stop the chain of destruction, but based on the level of destruction onscreen, you get the sense that almost the entire city is destroyed by the end of it. Then when Sean Connery confronts the villain afterwards, he says, "Venice still stands." No it doesn't! Finally, the last action sequence has no narrative structure at all. We have no idea what they're planning to accomplish or how, they just go into the enemy base and violence erupts. Then the place blows up thanks to the Invisible Man who secret placed bombs all over the complex. Great, so why did the other league members even need to go in there with him?
Lastly--and this is a big problem with movies about superhero "teams"--there are too many characters vying for the writers' attention for any one character to be adequately developed. Not that this movie doesn't give a valiant effort--there are several scenes dedicated to generating chemistry between the various characters in the league, but they feel stale because the characters pretty much only communicate in quips and cliches. Furthermore, the interplay between the league members never pays off. It doesn't nothing to raise the stakes as the movie goes on. Whatever relationships were established get tossed out the window by the end, which, as I mentioned, is just a lot of pointless, confusing action.
Bottom line, I loved this movie's visuals enough to overlook the boring, cliche script and cheesy dialogue. Watch it for the expertly filmed action sequences and nifty atmosphere. Just prepare to be emotionally detached from whatever's going on.