Just went through this, so I'll tell you what I did as it worked, but the mirror isn't as functional, but doesn't buzz/vibrate anymore.
First I ran a bead of clear silicone around the edge of the glass and plastic housing, about 1/4" onto the glass. Wipe the mirror down with rubbing alcohol or something first.
That helped some, but not enough when playing really loud. So I took the mirror off and taped up the openings and filled it with Great Stuff.
Now the mirror itself was silent, but I lost the nighttime flip mode, so you have to move it by hand, no biggie.
So then where the mirror attaches to the metal piece on the windshield would vibrate, so I took it off again and put a decent sized wire tie on the flat metal piece and slid the mirror back on and trimmed off the excess wire tie. This acts as a shim, so it fits tight and can't move/vibrate.
YES I'm extreme when it comes to getting rid of vibrations, but I don't listen to a lot of rap, so it can really take away from the music. I can play my shit at full tilt and have virutally ZERO rattles/vibrations in my car as many have noticed and commentd on.
Good luck...