I ran into this error today on an old ASA and i needed a quick fix that didnt involve downgrading any Java versions from the clients servers.
I can confirm that by using version 6.1(5)51 of the ASDM works correctly (as noted in the link below).
Just a quick tip.
Source: http://ciscoccvp.wordpress.com/2008/12/06/asdm-unconnected-sockets-error/