What does Montag continually hear overhead?
Montag continually hears bombers going overhead. It gets to him eventually and the reader learns some of his thoughts when he says or thinks the following:
"Every hour so many damn things in the sky! How in hell did those bombers get up there every single second of our lives! Why doesn't someone want to talk about it? ... Is it true, the world works hard and we play? Is that why we're hated so much? I've heard the rumours about hate, too, once in a long while, over the years. Do you know why? I don't, that's sure!"
The bombers serve a purpose in the story to remind the reader that the future society that Bradbury is writing about is on the constant verge of complete collapse or all out war. They add a sense of tension to the story as a whole. The unfortunate part about them is that nobody seems to care about them. Nobody seems to notice them even, and that bugs Montag. But perhaps the reason for that lack of attention is that the people simply just don't notice them at all. The entire society in the story is obsessed with filling every moment of silence or inactivity with some other kind of noise or entertainment. TVs are constantly on, headphones are in ears, etc. The fact that Montag hears the jets shows that he is in a way set apart from the society he lives in. That's also shown with his interest in books, too, but the jets are more subtle.