One of the people in the theater said that someone (maybe the killer?) got up and left the theater through the door 20 minutes or so before the killer came in. Hard to blame that on the theater.
The coming lawsuits will blame all sorts of things on the theatre, but all of them will definitely mention the door ~ that witness is going to be very popular.
Then the next thing he saw there was a guy dressed up and tossing grenades.
Yes, it's the door ~ Holmes had his car parked right there at the back presumably to make it easy to get his gear and guns.
There are door latch designs that cannot be defeated without sounding an alarm.