Okay, so Zeke's beard (which he used approximately 3 days ago in the meeting) in the locker means the medical bunker was either abandoned very recently, or that it was abandoned previously, but Zeke is still using it.

If it was abandoned recently, it could very well be related to the button not being pushed. I still think it was abandoned in a hurry. I think I saw a rocking chair left in the nursery.

The outer doors were covered over and hidden so someone left that way and covered it up. That does not mean that a bunch of people could not have come and gone through the "Escape Hatch" door - the exit could even be nearby somewhere.

As for the medicine cabinet being knocked over, that hints to me that someone else entered the medical bunker after it was abandoned looking for the medicine before Claire got there. That 'someone' pulled it over in a fit of desperate rage/frustration, perhaps? Desmond? (just wild guesses here)