Hey there. I pre-ordered two iPhone 4S phones - a black 16GB for me and a white 16GB for my wife - both of which have had this vibrate problem from the day I took delivery of them on October 14. The vibrate buzz drove me crazy because it was loud and the buzz cheapened the experience for me. I just expect more from my expensive iPhone. I do like the stronger feel of the new linear motor, though. Regardless, I ended up returning both phones and going back to my iPhone 4 because I couldn't stand the buzz. I was too worried about getting another one that did the same thing. (I am a bit OCD, by the way.) I'm sure Apple will quietly fix this problem in future manufacturing batches, so I'll wait a while and purchase again.
Anyways, before I sent the phones back, I did pop the back cover to see if I could determine what the source of the vibration was. I noticed that as soon as I put any pressure at all on the left side of the speaker enclosure, which is right below the new vibrate motor location, the buzzing stopped. I thought maybe it was the hard dock connector ribbon cable running over the top of the speaker enclosure rattling against the speaker enclosure, but it is adhered to the speaker enclosure, so that wasn't it. I tried everything I could think of to fix the buzz without disassembling anything, but couldn't do anything to calm it. I then thought that something beneath the left side of the speaker enclosure was rattling, but wasn't about to tear into the brand new phone that deep. So, I sent them back.
Well, I just replaced the home buttons in both of our iPhone 4 phones because after after 16 months, the phones weren't reliably registering home button clicks. (By the way, if anyone is having home button issues with your iPhone 4, replacing the home button will make the phone feel like new.) When I got to removing the speaker enclosure, I noticed it was only secured with one screw on the right side of the enclosure with no mechanical attachment on the left side. You can actually press on the left side of the speaker enclosure and watch it move up and down slightly. I checked out the teardown for the iPhone 4S and saw that the enclosure method of attachment is the same as the iPhone 4 - only one mechanical point of attachment on the right side. On the iPhone 4, the vibrate motor isn't anywhere near the speaker enclosure - it's at the top of the phone. However, on the iPhone 4S, the linear motor is adjacent to the left side of the speaker enclosure. I'll be willing to bet that the buzz is the left side of the speaker enclosure resonating against what is beneath it. I bet that if the speaker enclosure was removed and a small piece of double sided tape was placed beneath the left side of the speaker enclosure to mechanically attach it to what is behind it, the buzz would go away. If I would have discovered this before I sent my two 4S models back, I would have tried this. I wonder if you may be able to get the speaker enclosure out with only removing the battery, unhooking the dock ribbon cable, unhooking the antenna, removing the screw on the right side of the speaker enclosure and pulling it out. If you can do it without removing the logic board, then it might be worth a try.
This is a great forum, by the way!