In Harry Potter and the Prisoner of Azkaban, why does Remus Lupin take the train to Hogwarts? I do not recall any other instance of Professors taking the train. A basic search online yielded the following, unsatisfactory answers:
He was exhausted from a recent transformation.
I don't think that's it. He could Apparate, Floo, Portkey, all much faster and less exhaustive ways of travel. Dumbledore and the other Professors knew of his condition, and most were on good terms with him (seeing as several were also his professors when he was in school), it's likely they would have helped him with a quick, easy way to his new job without even his asking.
He wanted to see Harry in a not-teacher/student setting first.
Again, if this was such a big deal to him, he could have approached Harry a number of ways. In fact, Harry was staying at the Leaky Cauldron for quite some time. At any point, Remus could have casually met him there or in Diagon Alley.
He was put there specifically to keep an eye on students because of the Dementors.
Maybe? But if the school/Ministry wanted someone to watch the students around the Dementors, a lone, brand-new, tired-from-being-a-werewolf teacher doesn't seem like the best choice. Furthermore, we don't see any indication that any other teachers/adults were on the train (besides the conductor/train personnel).