If you run a version of Java JRE newer than v6 Update 10 (latest at this time is V6 Update 12) and see this error when trying to connect to a Cisco ASA ASDM interface: ASDM is unable to continue loading. Click OK to exit from ASDM Unconnected sockets not implemented. then you are probably running an older ASA software (6.1.5 released on 09-OCT-2008 and older ones have this issue) and you need to upgrade in order to fix this issue. Any version newer than 6.1.5.51 (that is the latest one available at this time) will work as expected. This version was released by Cisco to fix this issue on 16-DEC-2008.

The upgrade is simple and you can use my step by step guide for this; just keep in mind you will have to reboot do activate the upgrade. After this, your ASDM should be working again.