Unable to start Dropbox due to permission errors
Are you an administrator? If you are, try Chown and Chmod

Type the following into Terminal:

sudo chown -R yourUsername /Users/yourusername/Dropbox

sudo chmod -R 700 /Users/yourusername/Dropbox

If that doesn't work I'd run diskutil repairPermissions /

If those don't work, I would reinstall Dropbox.