Kree's got a nice set of posts about some of the more advanced problems with a DKP system in his guild (he calls them pitfalls, which works very well as a metaphor). I've never been part of a really serious DKP system, but just like with any other economy, DKP can lead itself to imbalances if you aren't careful with how people are getting and spending points.
Inflation is definitely a problem I've seen in other guilds -- usually, with DKP, you have a few very consistent raiders, and everyone else can fall behind. And eventually you get a few folks with tons of DKP, so much so that they can outspend everyone else and basically dictate how gear drops. Kree's solutions are good, though -- he offers up "point rot" (points devalue over time, so you can't save up tons of them at once), and a point cap (though even that can cause problems, as people are forced to spend DKP on gear they don't need rather than losing them). The other issues, collusion and upbidding, don't happen quite so often (both of those require players to be rather malicious, and in guilds where everyone knows which gear they should and shouldn't use, you don't usually have an issue), but he's got some good solutions there as well.
DKP was designed to make sure passing out drops is fair, and Blizzard has put all sorts of rules and restrictions in the game to try and get raiders the gear they need without a lot of fighting. As long as your guild remembers that there's always more gear to go around and that no one piece is worth stealing or causing trouble over, a good, balanced DKP system can help you avoid these alligator-filled pitfalls pretty easily.