Hm, Sounds like your opening the application from its original .DMG.
Open the DMG and drag Firefox into your Applications Folder.
If this doesnt work or you already have try this..
Find and check the access properties on the firefox profile. (What you say?!) Close Firefox - Click on your Main HD, users/your name/library/application support and remove the firefox folder from under the Application Support directory. Restart firefox.. that should do it.