This looks like a bogus error message. At least in my case, it was caused by a file ownership problem. To diagnose, I made a copy of TorBrowser.app, and was surprised when the copy ran successfully. Renaming the original to old, and the copy to TorBrowser.app, made it so that clicking on the onion TorBrowser_en-US in the doc auto-starts the browser (but still with a Vidalia UI glitch, it thinks Tor isn't running).
So as a short-term solution, you can try that. Or this is likely cleaner, if you are comfortable in Terminal:
Navigate to the TorBrowser.app directory, and do "sudo chown -R [user-name] Data", replacing [user-name] with your own user name. This changes the owner of all the directories/files in the Data directory, which is the one Tor is trying to get access to. (If what you have is a permissions problem, you might have to reset the permissions instead, for example with "sudo chmod -R ug+w Data", to add write permissions to files and directories for user and group.)
Details of my troubleshooting are below. I haven't figured out how the new version of Tor sorts out its browser from what used to be Vidalia, so I can't give clear instructions on how to make it all work in the least possible number of steps.
To figure out why the copy worked, I looked at the directory contents of both; the non-working directory had lots of file ownership of root and another administrator, whereas the successful one, specifically in the Data subdirectory, was entirely owned by my current account. The Tor browser modifies all sorts of files in its package. (This is a bad Mac practice, please note; ~/Library/Cache or some such should be used instead.)
I also know how it happened: When I was installing the Tor update, I switched from this account to another administrator account, before the download was completed. When the download completed, it unpacked and asked me if I wanted to install, but I was in the Admin account. So when I copied over the file I gave it privileges of that account, not of the account where the software was meant to be run. (This is a bit of a funky feature, I don't think the Mac user experience works quite right in this case.)