OS X Lion - How to configure website on Apache
The default permissions on ~/Documents don't allow anyone but the owner access to it. Apache accesses the documents as the _www user, so if that user can't get to the web folder, you'll get a permissions error.

If this is the problem, there are a couple of possible solutions: you can either move the project folder outside of ~/Documents (e.g. /Users/me/workspace/mySite), or change the permissions on ~/Documents to allow Apache in (chmod +a "user:_www allow search" ~/Documents should do the trick).