What browser are you downloading with?

Are you using the About dialog updater or the install package on mozilla.org?

If one way of updating fails, you can try one of the other ways.

• SEE: the Update Firefox to the latest release and How to fix the Update Failed error message when updating Firefox articles.

If there are problems with updating or with the permissions then best is to download the full version and trash the currently installed version to do a clean install of the new version.

Download a new copy of the Firefox application and save the disk image file to the desktop

• Firefox 27.0.1: http://www.mozilla.org/en-US/firefox/all.html

• Trash the current Firefox application (open the Applications folder in the Finder and drag the Firefox application to the Trash) to do a clean (re)install
• Install the new version that you have downloaded
• https://support.mozilla.org/kb/Installing+Firefox+on+Mac

Your personal data is stored elsewhere in the Firefox profile folder, so you won't lose your bookmarks and other personal data when you uninstall and (re)install Firefox.

• http://kb.mozillazine.org/Profile_folder_-_Firefox