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.

From http://hints.macworld.com/article.php?story=20130315064419386

It turns out that Dropbox has a hidden feature to fix such things. Open the Dropbox preferences, click on Account, then press the Option key. The Unlink This Computer button will change to Fix Permissions. Click that button and let Dropbox go through your files.

I saw the same error message and had the same issue where Dropbox wouldn't start on my laptop so I couldn't access the hidden Fix Permissions feature. I tried fixing the permissions manually with Terminal. I also tried uninstalling and installing. I also tried removing the .dropbox folder in my root folder. Nothing worked.

Finally, unlinking and relinking my laptop remotely via the Dropbox website fixed it. When I started Dropbox again, I signed in and my Dropbox folder started syncing again. Article on Dropbox's help site walks through the steps and has suggestions for how to relink the files if the Dropbox location has changed.

Good luck!