I have resolved this problem.
There was a particular folder that was owned by someone else which I had moved. It contained a .dropbox dotfile, which I deleted. I then moved the contents out the folder and deleted the folder.
Steps to replicate.
1. Create shared folder
2. Invite multiple people who must accept
3. Place large data in folder, e.g. 20 files of 50 mb each
4. One of the persons accepting the sharing invite must move and rename the folder
5. Same person as in (4) must add data to folder
6. Folder never finishes syncing. Dropbox.app maxes out CPU on Mac OS X
7. Go into folder on CLI, delete .dropbox (so as to unshare it), rename folder, move contents out, delete folder.