I guess I am a little curious about the "initial" problem faced by Montag. I could easily talk about the novel's big main problem, but Montag's first problem might be different to different readers.
When the book opens up it's clear that Montag likes his job. He likes burning books.
"IT WAS A PLEASURE TO BURN IT was a special pleasure to see things eaten, to see things blackened and changed."
Montag has no problems with what he does, but on his way home that night he meets Clarisse. I think she is the initial problem. He is a bit attracted to her, which is a minor problem, since he is married already and she is 17. Of course I guess that points to problems with his marriage, which I'll get to in a minute. But the main thing that Clarisse does is make Montag question his job and his passion. She does this with one question. "Are you happy?" And that basically kicks off the rest of the novel, because let's face it, Montag is not happy. For starters, his wife is addicted to TV, music, and sleeping pills and she can't carry a conversation about anything other than the first two things. His boss, Beatty, is belligerent and belittling. No, Montag isn't happy and can't figure out why someone like Clarisse is so happy. I think that is the initial problem of the novel.