I have come across a few questions on this site where people ask "how did x store/take out y from the Mirror?", so were the things actually stored in the Mirror?
Yes, all evidence points to the fact that Dumbledore stored the Philosopher's Stone inside the Mirror of Erised.
We know that the original purpose of the Mirror was to show the viewer their "heart's desire". However, according to JKR, Dumbledore specifically changed the enchantment on the Mirror to "hide" the Stone in it:
Only after Professor Dumbledore makes key modifications to the mirror (which has been languishing in the Room of Requirement for a century or so before he brings it out and puts it to work) does it become a superb hiding place, and the final test for the impure of heart. src
The term modifications implies that hiding the Stone was not done by using the Mirror's original purpose at all; it was something else, a different behavior that that Mirror was updated to perform. And given that Dumbledore specifically changed the mirror to be a hiding place, the most reasonable explanation is that he turned it into that hiding place directly.
As a tentative answer, I don't think that's the case.
As a similar example, take the Sorting Hat.
When a true Gryffindor showed need of the Sword of Gryffindor, they could pull it out from the hat. That means it was just wired that way, that the said person received the Sword, through the Hat. Similar was the Room of Requirement, which provided something that a person wished. We know, in the Sword's case, that it was stored in Dumbledore's office, behind his desk in the glass case.
The Mirror was just a magical medium of showing one's true desire, the person just needed to 'tweak the desire', to trigger the outcome.
I wouldn't say he stored the Stone in the Mirror of Erised. As we know, the Mirror shows each person their deepest and most desperate desire of the heart. While I agree with @MikeEdenfield in that Dumbledore used the enchantments of the Mirror and tweaked them slightly to protect the Stone, I wouldn't say the Mirror was storing the Stone. As Dumbledore tells Harry in Harry Potter and the Philosopher's Stone, Chapter 17: The Man With Two Faces
You see, only one who wanted to find the Stone – find it, but not use it – would be able to get it, otherwise they’d just see themselves making gold or drinking Elixir of Life.
I think Dumbledore enchanted the room as well, in connection to the mirror. If the Mirror recognized somebody's desire to "find the Stone, but not use it" it would trigger the charm in the room. The Stone was hidden in the room by a controlled Vanishing charm, causing the Stone to reappear when triggered by the Mirror. Dumbledore definitely used the Mirror to hide the Stone, but not to store it.