Normally, disfiguring a PC is one of those "never do it" rules of thumb. (for you obstinant folks, yes, there are exceptions).
However, determining game impact is quite a different thing. I would be concerned about adding injury to insult (yes you read that right).
HP: normally represents a bunch of "just a flesh wound" hits, and not a representation of the physical body. I'd be wary of trimming HP for limb loss, because, once healed, the PC is just as dodgy, tough as normal, there's just less target
AC: there's less target, one could argue there's less to hit. Considering size modifiers deal with this for Medium to Small creatures, there's some merit there. However, being one limb smaller is a not a significant change compared to a full size change.
Dex: I don't think PC would be less dextrous. But, they would have difficulty doing some things, in a similar fashion as wearing armor impacts certain skills. Maybe make a -1 Armor Check penalty (or whatever it's called). Enough to impede certain skills. Not enough to impact AC in combat or saving throws.
Without affecting any game stats, losing an arm has some obvious game effects. For one, you can't hold two items at once. This means no dual weapon, no shield & weapon, no weapon & potion. Changing items is definitely more tedious, justifying AoO's. All the two-handed weapons are unusable (barring a Feat to do otherwise).
I'm a big fan of not jacking with a PC or their stats. If a PC loses a limb, just letting the obvious non-game stat effects take place will more than likely alter that PC in many ways (as I describe above). it also gets the DM out of being a rules designer, which is risky business if done poorly.
Lastly, in the old days there were folks who wanted STR penalties for female PCs because they were weaker. We got away from that mentality, which pleased all the body-building women who could kick the average gamer's arse. I suspect the one-armed folk of the world would also appreciate not having the game system portray them as "lesser" entities compared to other folks, otherwise. I'm not advocating being PC to appease anybody, just saying, let's not make rules to figure out how much having one arm makes your PC suckier than mine. There's some obvious impacts, otherwise, leave it alone.
