FULL PRODUCT VERSION :
Java(TM) SE Runtime Environment (build 1.8.0_77-b03)

ADDITIONAL OS VERSION INFORMATION :
Windows 10 64bit (Version 10.0.10240)
Windows 7 64bit

EXTRA RELEVANT SYSTEM CONFIGURATION :
This bug occurs on Windows 10 64 bit and somewhat less often on Windows 7 64 bit. (32bit not tested).
It does occur in Firefox 42 to 45. It does not occur in Firefox 40. I am not sure, if it occurs in Version 41. Version 46.0b9 is affected. Nightly (48.0a1) seems to be not affected.

A DESCRIPTION OF THE PROBLEM :
Firefox' "do you really want to run this application"-dialog hangs.

This issue has also been reported to mozilla. https://bugzilla.mozilla.org/show_bug.cgi?id=1263130
Benjamin Smedberg [:bsmedberg] resolved it as "RESOLVED WONTFIX" with this comment:

This is an unfortunate but expected side effect of moving the Java plugin into a separate process like all other plugins. The Java plugin needs to change the way it does modal dialog boxes so that it stops blocking the browser event loop. Until that time there is no suitable fix for this problem.

Please file this issue with Oracle.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
.....

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
Java Plugin starts an applet.
ACTUAL -
Jva Plugin hangs. Firefox kills the plugin.

REPRODUCIBILITY :
This bug can be reproduced always.

CUSTOMER SUBMITTED WORKAROUND :
Click "don't ask me next time" when loading the applet. Only this dialog hangs.