The wrong dates appear to be a rare sporadic problem, but nothing to worry about. See https://bugzilla.mozilla.org/show_bug.cgi?id=594528

The actual problems you are having with Firefox hanging at shutdown need to be focused on.

Does the problem happen in Diagnose Firefox issues using Troubleshoot Mode?

Some possible reasons for a hang at exit can be found here: https://support.mozilla.com/en-US/kb/Firefox+hangs#Hang_at_exit

This happens if the updater wasn't able to retrieve the date from the OS and used 0 (zero) instead.

Firefox uses the Unix EPOCH that starts with Jan 1, 1970 and that date is corrected for the time zone.

See http://en.wikipedia.org/wiki/Unix_time

I didn't know there was a safe mode for Firefox, I'll tr it and see.

I've been using safe mode for several days now trying to get it to do the same thing and so far it hasn't. It seems to work fine in safe mode. The few times I went in the regular way it would do the same thing. So does this mean one of my the add ons are to blame for the issue? I did check to make sure I didn't have any of the add ons listed in the link for possible reasons for hang ups.

Firefox safe mode is meant for diagnostic purposes and not for permanent usage.

Possible suspects can be the BitDefender extensions (BitDefender QuickScan, BitDefender Antiphishing Toolbar) and plugin (BitDefender QuickScan Web Netscape Plugin)

You can also remove the Java Console extensions and disable the Java Quick Starter extension.
See http://kb.mozillazine.org/Java#Multiple_Java_Console_extensions

Disable the Java Quick Starter extension: Tools > Addons > Extensions Control Panel > Java > Advanced tab > Miscellaneous >Java Quick Starter (disable)

See http://www.java.com/en/download/help/quickstarter.xml - What is Java Quick Starter (JQS)? What is the benefit of running JQS? - 6.0

If it does work correctly in Safe-mode then disable all your extensions and then try to find which is causing it by enabling one at a time until the problem reappears.
See Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems

I admit I used safe mode probably more than I should but since the problem didn't happen every time I was trying to get it to happen in safe mode, which it never did. I disabled all of the BitDefender extensions but it was still happening. I did read about the Java Console extensions but I'm unsure what would happen if I disabled all of them. I have 6.0.20 & 6.0.21. I also have in plug-ins: Java Deployment Toolkit 6.0.210.7 & Java (TM) Platform SE 6 U21 (6.0.210.7.).

I then read about the Java Quick Starter and it's referring to 6.0. The one I have in extensions is 1.0. I did disable this Java Quick Starter.

After disabling the JQS, I was able to click out of Firefox and bring it back up twice without a problem. It may be a coincidence but I am hoping that was the problem. Now, what about the Java Console extensions? Do I leave those alone or should I disable them as well. Thanks for your help on this.

No, you do not need the Java Console extension either. The Java Console extension is for debugging Java applications and normal users do not need it. In the past that extension was hidden (not visible) in Tools > Add-ons > Extensions, but current Firefox versions no longer allow extensions to hide their presence.

Thanks for all of your help. I'll get rid of the Java Console also.