Profile missing after using Migration Assistant on Mac OS
From MozillaZine Knowledge Base
When you use Apple's Migration Assistant to transfer all of your files, programs, and settings to a new Mac computer and you try to open Firefox, users report getting a "Profile Missing" dialog box which says: Your Firefox profile cannot be loaded. It may be missing or inaccessible. This will also occur when attempting to start the Profile Manager.
This issue can be caused by a problem with permissions in your Home folder. The problem is that most utilities (including Disk Utility, for some reason) don't repair permissions in the Home Folder. To resolve:
A user reports the following solution: 
Another user reports this solved the problem: 
You need to open the Terminal application in the Utilities folder. At the command line prompt enter or paste the following command line:
sudo chown -R `id -un`:`id -gn` ~
Press RETURN. You will be prompted to enter your admin password which will not be echoed.
Once you do that, Firefox should open the profile folder and you should be ready to go.