Check the bookmarks to make sure that they are correct. Then try to reset Firefox. Make sure before you reset that you have backups of your stuff first. Bookmarks and passwords should be safe, but you will lose everything else. Firefox Options > Help > Trouble Shooting. The reset is at the upper right.

Try the Firefox SafeMode to see how it works there.
A troubleshooting mode, which disables most Add-ons.
Troubleshoot Firefox issues using Firefox SafeMode

When in Safe Mode...

• The status of plug-ins is not affected.
• Custom preferences are not affected.
• All extensions are disabled.
• The default theme is used, without a persona.
• userChrome.css and userContent.css are ignored.
• The default toolbar layout is used.
• The JIT Javascript compiler is disabled.
• Hardware acceleration is disabled.

• You can open the Firefox 15.0+ SafeMode by holding the Shft key when you use the Firefox desktop or Start menu shortcut.
• Or use the Help menu item, click on Restart with Add-ons Disabled... while Firefox is running.

To exit the Firefox Safe Mode, just close Firefox and wait a few seconds before using the Firefox shortcut (without the Shft key) to open it again.

If it is good in the Firefox SafeMode, your problem is probably caused by an extension, and you need to figure out which one.
http://support.mozilla.com/en-US/kb/troubleshooting+extensions+and+themes
Or it might be caused by Hardware Acceleration.

When you figure out what is causing that, please let us know. It might help other user's who have that problem.

Are you middle-clicking the bookmark to force it to open in a new tab?

You can check for problems with the places.sqlite database file in the Firefox profile folder in case some bookmarks are corrupted.

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
• https://support.mozilla.org/kb/Bookmarks+not+saved#w_fix-the-bookmarks-file