In Fahrenheit 451 what dangers and disadvantages does Montag face when he goes on the run after killing Beatty?
As Montag is on the run, he faces several dangers. The most terrifying danger is that of the mechanical hound, who has Montag's scent, and is on the trail. The hound injects a deadly poison, and has already almost gotten Montag on the leg. The hound's super-tracking skills are almost inevitably going to catch up to Montag.
Another threat comes from the media; the government took quick advantage of the fact that almost everyone in their society stays home at night and watches television. They used the program signals to send out the alert that Montag was on the loose, encouraging them to report anyone or anything that they see that is suspicious, that might lead them to Montag's house. As he runs, he can see inside people's windows, and realizes that there is live footage of his escape, and his picture, posted all over the televisions. At any point in time, someone could look out their window, recognize him, and report him. He is literally being hunted by a death machine in the mechanical hound, and surrounded by potential betrayers absolutely everywhere he goes. Once taken, he will most likely be killed or locked away for life.
Once he gets to Faber's house, the danger increases to include his friend Faber. His scent will lead the danger right to Faber's doorstep. They try to cover Montag's scent as best they can with Faber's own, and with alcohol. But, the danger is still there, and now Faber is part of the equation. Montag flees the city under all of these dangerous circumstances. I hope that helps a bit; good luck!