This clip is Hollywood fiction, but there is enough evidence around to suggest that fiction will soon become reality. Right now the discussion is not about whether we can or cannot do face transplants, but when we will be able to do them. Even if the people who think we can do it now are wrong, it can't be too far away, so the real question is not "Can we do it?", but should we do it?.
Freakin out.
Interestingly, one of the key objections put forward against doing it is that you would look too much like your donor, and that freaks people out a bit. In the movie the whole thing is about John Travolta looking like Nicholas Cage and vice versa. But with a real face transplant that won't be the case. Everyone's bone structure is different, so putting my face on someone else's bone structure is going to look totally different. Imagine if you put Mattingly's skinny face over Norman's boof head. Its going to look different - ugly, but different. So that's a bogus argument. .
So what are the other possible objections? One put forward is that your face somehow defines your personality, so somehow you are morally cheating by putting on a different face. You can talk about judging a book by its cover, and beauty is only skin deep blah blah blah, but the real problem with that argument is a bit deeper than that. The real problem is from the fear that we will lose some of our interpretation skills when confronted with a false face. Facial expressions do help us interpret messages from the other person. A tight grin, a creasing of the eyes, a blush - they all help us judge whether the words we are hearing are true or false. Not being able to rely on those skills means that we will lose some of that sensory perception.
The other main argument raised against face transplants is that once we start something, inevitably it leads to improper use, like cosmetic surgery etc etc. Basically we don't think we can trust ourselves to use technology or medical advances in the way they were intended.