When Montag opens the cage door be pressing a button with his forefinger (presumably it's a fingerprint reader), he exits the cage and closes the door behind himself, but it then pops open rather than securing.
It doesn't make sense that Montag would change into civilian clothes and then stow his gear (flamethrower) in the armory. Normally one would be have to be in uniform until end of shift. Perhaps this is a setup for later on when he enters the armory in civilian gear to pick up a transponder.
At around 54 Minutes into the Film, Michael Shannons character Cpt. Beatty speaks to his men with a megaphone. This scene is completely mirrored, as Beattys Leathercoat has his Button Row now on the left side, and the 451 on the Fire-Truck is mirrored, too.
Just after the 7:20 mark, a 360 bumper shot occurs then jumps to an overhead shot looking down on the fire engine; The camera is visible on an arm attached to the front bumper before disappearing in the next shot.