Add-ons can interfere with the right-click menu. Try running Firefox in Firefox safe mode, this will disable extensions and themes and can be used to see if they are causing the problem. If it works in safe mode, follow the procedure in the Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems article to identify which one is causing the problem.

There are other things that need attention:

You have or had an extension installed (NET_mmhpset) that has changed the user agent from Firefox/3.6.13 to Firefox/3.5.5.
Mozilla/5.0 (Windows; U; Windows NT 6.0; en-US; rv:1.9.2.13) Gecko/20101203 YFF3 Firefox/3.5.5 NET_mmhpset ( .NET CLR 3.5.30729; .NET4.0C)

You can check the general.useragent prefs on the about:config page.
You can open the about:config page via the location bar, just like you open a website.
Filter: general.useragent
If general.useragent prefs are bold (user set) then you can right-click that pref and choose Reset.

See:

• Web sites or add-ons incorrectly report incompatible browser
• Find what version of Firefox you are using

• http://kb.mozillazine.org/Resetting_your_useragent_string_to_its_compiled-in_default