Does it bother you?

no cause he grew more and more inhuman has time went on...

Not really because if you think about it, he was using Quirrell as a body and not a horcrux. Maybe he has a nose before Harry defeated him for the first time. His horcrux probably took away his nose.

Either that, or the director didn't think of getting rid of his nose.

Have you checked the book?

Not really.