We know that the Department of Mysteries is one of the most secretive and dangerous departments in the Ministry of Magic. People who work there are sworn to secrecy and known as Unspeakables. You'd have thought that the security of such an off-limits area would be fairly tight. Yet when Harry turns up he is able to simply walk inside.
Harry turned toward the plain black door. After months and months of dreaming about it, he was here at last...
He turned to face the door and walked forward. Just as it had in his dream, it swung open and he marched forward, leading the others over the threshold.
(Order of the Phoenix, Chapter 34, The Department of Mysteries).
Were there no defensive charms or security spells in place to protect the Department of Mysteries from unvetted outsiders? If not, the Gryffindor commonroom was better protected. At least that had a password! Or can it be assumed at there were defensive spells in place but that these had already been disabled or overridden by the Death Eaters?
Non-Ministry staff have to submit to an inspection at the security desk on arrival. However, it'd be easy to gain admission to the Ministry by claiming to be visiting another department but then actually go down to the Department of Mysteries. Another option would be to go the Ministry at night and simply evade the security personnel, as Nagini did. The rotating hallway offers some security by disorientating outsiders. This merely confuses people, though; it doesn't stop them from entering. Harry and co were able to find the room they were looking for after a while through trial and error. I'm interested in if there's any additional security that applies to the Department of Mysteries and its entrance beyond what's listed here.
The fact that the Order of the Phoenix spent a considerable amount of time trying to guard the DoM entrance may be suggestive. They clearly felt that the prophecy was vulnerable on some level.
Are there any security measures that protect the Department of Mysteries? If there are, why didn't Harry run into them? If there aren't, why did the Ministry not consider its secretive department worthy of any protection?