Good start, but let's see it go further!
For a "story" about a corrupt group of businessmen running an evil competition for their own amusement, the level of violence is played down. Enemies go down with a small spray of blood, but nothing excessive. I don't usually approve of over-the-top gore, but this would be one setting where it would be entirely appropriate. An amped-up level of carnage would better submerge the player in what is supposed to be a vicious fantasy. Let's have some more flying blood, severed limbs, or location based damage!
I'd also like to see more interactive enviornments. While your character can smash through a few doors, or bounce bullets off certain surfaces, the rest of the lavishly detailed world remains untouched by the destruction raining around it. Having a hostile enviornment, such as enemies going over the many elevated walkways, molten steel dripping in the wharehouse, or buildings collapsing in the warzone would have made the whole affair feel more dangerous.
The melee combat, as mentioned in other places, badly needed to be re-thought. At best it's clunky, at worst it's useless. There are several characters listed with "high strength", which is nearly useless in a game where there's only a single clunky melee attack. How about a close-combat system, CQC weapons, or hold manuevers. How exciting would it have been to be able to use a thug as a human shield in the siege levels?
Additionally, for a game all about stylish shooting, there aren't all that many stylish moves you can do. Other than shooting people in the head, rolling around clunkily, or shooting people from far away, there's no real variety in how your character moves through the world. If the combo mechanics of The Club were mixed with a more stylish third-person shooter (such as Max Payne or Stranglehold) the mix would feel fresh and considerably more re-playable.
That said, the game remains strangely addicitive and enjoyable for about a solid weekend. The Club seems to be almost tailor-made for a weekend rental. Fans of fast-paced shooters will certainly enjoy themselves while the fun lasts.