Couple of things regarding his speed.
1) He'd be faster if he dropped a few kilos.
2) The leg break took place years ago, and he's had plenty of time to heal from it. Furthermore, it's not really robbed him of his speed. He's still pretty quick in terms of acceleration but you don't see it too often because a) He doesn't play as advanced a position for us and so very rarely finds himself in positions where he's up against the last defender b) Defenders in the premier league are much better then in Portugal.
Anderson's problem isn't that he's got a lack of pace. Rather it's his inconsistency. You just don't know which Anderson is going to show up (now that I think about it, this seems a very Brazilian trait). On his day he can put Gerrard and Fabregas to shame, but then there are occasions where he looks atrocious even against relegation caliber midfielders.
Add to that the lads complete inability to score and just average passing range and you get a player who's performance during the course of a game can run from the sublime to the dreadful.