After taking the Java update via the App store, Matlab will launch and open the last file, however, it will freeze and don't open any file. This is a Java issue and reinstalling Matlab or a new user profile will not resolve.
Context - Affects MATLAB 2012b and earlier, with the Java for OS X 2013-004 update - The original update gives build 1.6.0_51-b11-456-10M4508 - This can be verified by running the command below in terminal and comparing the build
$ java -version
Good:
Java(TM) SE Runtime Environment (build 1.6.0_45-b06-451-11M4406)
Java(TM) SE Runtime Environment (build 1.6.0_51-b11-457-11M4509)
Bad:
Java(TM) SE Runtime Environment (build 1.6.0_51-b11-456-10M4508)

SOLUTION - Apple's update has been fixed, however, it is not being pushed via updates to clients already affected. It is now safe to update via the Appstore, Java for OS X 2013-004 is the package. - If you are stuck on version 10M4508, you can manually update:
* for 10.7/10.8: http://support.apple.com/kb/DL1572
* for 10.6: http://support.apple.com/kb/DL1573

Tags: Matlab, Java update, Mac OS X