I have finally done the tests with a brand newly created account, as well as booting from a different disk.

When I create a new account and run WireShare 5.6.4.1, the same previously reported issues remain (pesky window indicating "WireShare has encountered an internal error" and no connection).

When I boot from a different disk (pendrive in which nothing except the Mac OS X 10.9.4 Mavericks was installed), I installed the latest Oracle Java 7 (1.7.0_67) and WireShare and all worked fine (no pesky window and turbo-charged connection in less than one minute). Both for 32- and 64-bit mode.

If then I install Java 6 (1.6.0_65) on such pendrive, the pesky window does not show, but I get no connection. For both 32- and 64-bit mode WireShare always shows Java 6.

When I uninstall Java from such pendrive and re-install Java 7, all works again.