Here's the basic set up. All these exit doors are usually wired into the office, and sometimes up to the projectionist's booth, and sometimes even to a panel near where the head usher is situated, so that a light goes on when opened. It is expected when a movie ends, and so would not rate extra attention. But during a show, and for more than a few seconds, is when someone would be sent to check. The usual culprits are someone letting friends in the back. There is no need to disable the alert that the door is open. These are also not as the emergency exits we see at the back of a retail store, that are loudly alarmed.
Virtually ever Cinema will have an alarm system for when it is truly shut down for the night. That would include a sensor on every door to begin with. So having it also as able to register just as "open" during normal hours is not a stretch.
The easiest way to prop one open is such as a piece of wood. All these doors have the panic bar, which begins to engage once the door is closed to within about 1/2". The open alert is simply a pair of magnets at the top, which enable/disable a circuit. Had Holmes scoped it out first, say earlier in the week, he may have tested such, that is seeing if he could prop it open, and if anyone reacted after 5-10 minutes. Or, if he checked closer, most panic bars have a hole, in which you can insert an allen wrench, and once depressed in the "open" or "unlocked" position, then lock the bar open with a half-turn. It is still potentially a little problematic to open from the outside, as it closes flush, and there is no handle. But it would register as "closed" while also being unlocked.
I suspect that the theater had the magnetic sensors on the doors, and a system which indicated that the door was open. That is more standard than not. And that they didn't notice, perhaps understaffed with the midnight showings, or not paying attention, etc.
