This fix was the result of me asking about replacing my side mirrors. Since I did this fix and found it to work perfectly, I wanted to place this topic in the maintenance section with a proper subject heading so that guys can find it with a proper search.
Hat tip to SAURON327 for the link for this fix. http://www.camaros.net/forums/showthread.php?t=195512
If you want to avoid going to the link or if it is no longer good, here is what you do:
Get a pan that will fit your mirror sitting in it mirror side down. I used a pie pan. The article said to use mineral spirits, but I didn't have any so I used lacquer thinner. Pour just enough to cover the mirror up to where the glass would be and set the mirror face down in the spirits or thinner. The first mirror I only waited an hour or so and when I picked up the mirror and shook it, I could feel the mirror "rattle" and so I got a feeler gauge and pried it out. It came out easily, but I could feel the grinding of the glass and it felt as if the mirror could very easily crack or chip, but it did come out. The other side, I let it stay in overnight and the next day when I picked the mirror up, the glass and 4 "blobs" of saturated double sided taped were left in the pan.
My mirrors had rivets, so I set my mirror in a vice with a heavy rag and tapped both of the rivets until they were tight against the metal strip. I didn't need any loctite or anything after that, but did add a couple of drops from the inside just in case it might help a little. Finally, clean the glass and mirror, new double sided tape, and press mirror back in. DONE.
It was quite easy and is the proper way to repair these things. So, if your mirrors are floppy and you don't want to buy new ones....this will work.