Update: This issue has been resolved, you should no longer have problems with patch downloads from MOS. Also, if you have not looked at supporthtml.oracle.com (the non flash version), it has been dramatically improved.
Since the switch to My Oracle Support, I have been unable to download patches from E-Business Suite 12.0 via the My Oracle Support pages (both flash – it seems to only give me the R12 that points to 12.1, and html – it doesn’t give an EBS patches). Fortunately, the html version of updates.oracle.com still works. An easy way to connect is with http://bit.ly/OraclePatches. You will still need to be logged in to the Oracle SSO account that is linked to My Oracle Support.