I've never played Mirror's Edge so it has no bearing on my opinion of Assassin's Creed 1 (which I haven't finished). But Altair does have all his fingers, I have watched his hands closely in the pan when you synchronize the map to reveal more of the area you're in.
I just wish he'd stop fucking crouching like he's taking a piss. It bugs the hell out of me.
Fighting in the game...was not as fun as it was in Splinter Cell (Ubisoft is responsible for both the SC series and Assassin's Creed, but that's like common knowledge), but I did like the one-hit-kill counter moves Altair had...when he wasn't repeating the same move 100 times in a row.
It also annoyed me that if you got on a horse you would immediately switch to your sword and it wouldn't revert to your hidden blade or curved knife upon dismount. I blew like 12 stealth kills like that and decided it'd be funnier to push people to their doom.