27-inch iMac on a wobbly floor I have set my 27-inch iMac on a desk on a wobbly floor with a thick carpet. When people walk in the room, the desk tends to shake, and so does the iMac. 

I worry that the joint between the iMac and its integrated stand might be damaged due to the vibration. Could this be a problem?
If your wall is more stable you could always get a wall mount for it. They cost around $30-$40 on Apple's site. For the money it would be worth a try, or move the iMac somewhere sturdier in your house possibly. If the integrated mount were to somehow fail, the shag carpet might help minimize any resulting damage.