I don't have a problem with his current face, what bugs me is the total absence of facial expressions. I mean he doesn't even move his eyes, nothing. Always staring straight ahead, no head turning, he only blinks in a weird way that doesn't really make his eyelid to move, the texture is just dragged down like it's pulled down by a fishing hook, looks terrible.
Head doesn't move when the player moves his mouse etc. Absolution had way more polish. But I get that, they really cut the funding this game received, and I prefer this technically poor version of Hitman than no hitman at all.