What are some conflicts that result from people caught reading in Fahrenheit 451?
One of the most important conflicts caused by reading is the old woman whose house is full of books and magazines. Montag, who has been a fireman for ten years, is used to the book readers being removed by police before they arrive; this lets them have no care for the people they are punishing, only the material books. However, this call comes in daylight, and the old woman is still there. Montag discovers that his job, which has always come naturally, is now tinged with unease:
But now, tonight, someone had slipped. This woman was spoiling the ritual. The men were making too much noise, laughing, joking to cover her terrible accusing silence below. She made the empty rooms roar with accusation and shake down a fine dust of guilt that was sucked in their nostrils as they plunged about. It was neither cricket nor correct. Montag felt an immense irritation. She shouldn't be here, on top of everything!
(Bradbury, Fahrenheit 451, Google Books)
Montag's realization is that his job harms people, not just "things," and he is not happy with that epiphany. The firemen are not simply enforcing the law and removing contraband, they are destroying the lives of actual individuals. Montag has never considered the individual in his actions and his job, only the job itself, and now he is conflicted between his proper position in society and his own growing individualism. With the old woman's death his job becomes distasteful; Montag can no longer justify his actions by the approval of society.