You only see context menu items if they apply to the situation and if you right-click an image then you can't search for text on internet. That is only available if some text is selected.
The same for Copy Link location that only appears if you right-click a link and images may not have a link that opens if you would open if you left-click this image.

Note that Firebug has been mentioned to cause issues with the right-click context menu, so make sure to have the latest updates of all extensions.

You can create a new profile as a test to check if your current profile is causing the problems.

See "Creating a profile":

• https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues

If the new profile works then you can transfer some files from an existing profile to the new profile, but be careful not to copy corrupted files.

• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

I had this same problem, and I do have Firebug. I opened the addons page and told firebug to find updates. It gave me no feedback. I restarted firefox in case there was a pending addon update, and the issue is resolved. Thanks for your help.