If you were a Star Wars fan in the early days, you undoubtedly heard that Mark Hamill was in a car accident around the time that the first movie wrapped filming. You may also have heard a wide variety of stories about the damage done (or not done) to his face, when the accident occurred and what impact it had on the filming of the second movie.
Authoritative answers to those questions don't seem to be forthcoming, in large part because Hamill himself seems to have told conflicting stories. At the time, he reportedly told Dynomite magazine that the accident had "made hamburger" out of his face; years later, he seemed dismayed at the stories surrounding the accident and said that he'd only broken his nose.
Whatever the details, the truth is that Mark Hamill returned to film the second and third movies looking pretty good; there's nothing about him at all that says "guy who smashed his face in a bad car accident". Though there was a lot of talk at the time about how different he looked in the second movie (I'll admit that I didn't think he was as attractive in the latter films), I showed before and after pictures to my teenage daughter who knew nothing about the accident yesterday, and she didn't see any difference. Or rather, she attributed the slight difference she saw to something intentional that fit the story.
These are the pictures I showed her: Mark Hamill Before and After.
Looking at these two pictures next to one another, it's clear that Hamill's hair is darker in the later films--something I'm not sure I noticed at the time. He also has an older, harder look--but my kid not only suggested that this fit the movies and might have been intentional, but pointed out that we see the same kind of change in Anakin between Revenge of the Sith and The Clone Wars. In other words, it might very well have nothing to do with any damage or reconstruction Hamill may or may not have undergone.
I'd have to say that if there is a change, it's not significant enough to have harmed his career based on his looks--but based on the rumors and perception? I'm not sure.