This Problem ist fixed with ASDM Interim Release 6.1.5.57 asdm-61557.bin. From Release Notes:
Fixed: „ CSCsw43498 ASDM is not working with Java 1.6.0_11 and Vista OS “
According to the bugreport you can also:
as a Workaround
I had problems to connect to Cisco ASA Firewalls.
ASDM cannot be loaded. Click OK to exit ASDM. Unconnected sockets not implemented
Just deinstall the Java 6 Update 10
Change the link /usr/bin/java to the apropiate version
Solaris 10 comes with JDK 1.5.x which does not work with ASDM. But you can install JDK 1.6.0_7 (but nothing newer).
The Java version on a Macs is still 1.6.0_6 (on Intel Dual Core)
=Utilities/Java > Preferences=