hello, probably one of your installed extensions was interfering here - you can test that by trying to replicate this behaviour when you launch firefox in safe mode once...

Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems

Problem with frozen / unselectable tabs applies to PCs as well, the extension that was affected by Firefox 29 is
How Many Times Can I Back? :: Add-ons for Firefox

You will have to disable the extension for now. I see you went back to Firefox 28 (a lot easier on your health). It was really a pain trying to switch tabs strictly through the "List all tabs" drop-down, and use Ctrl+T, and Ctrl+W (or for you with the Mac Cmd key ⌘ ).

I had the same problem, it is now reported in
Problematic extensions - MozillaZine Knowledge Base

Firefox 29 made changes to Tabs, and removal of the Addons Bar. since you also show Status-4-Evar in your "MORE SYSTEM DETAILS" you use the Addons bar and have a problem there as well. You also have another extension one with the word "tab" in it "Old Firefox Tab 1.0" which could be affected as well.

Either of these extensions will restore the addons bar, I prefer The Addon Bar (restored) which I prefer because I have tabs on the bottom.

Those who can stand tabs on top and the hugh Firefox button may prefer
Classic Theme Restorer (Customize Australis) :: Add-ons for Firefox
I see you did try that when you were on Firefox 29.

Both extensions preserve "Ctrl+/" shortcut to toggle the Add-ons bar.

To restore Tabs on the bottom (in Firefox 29)
Tabs on Bottom (Australis) :: Add-ons for Firefox

If you look in your "MORE SYSTEM DETAILS" in the right hand panel you can see what see of the extensions and plugins that you have. For instance
How Many Times Can I Back? 0.2.2011012001 ([email protected])
Old Firefox Tab 1.0 ({b4b3e886-52d2-11e3-b4ad-f2ea6188709b})
Status-4-Evar 2013.10.31.22 ([email protected])

I'm working through my own problems and will be able to use Firefox 29 even though some of my toolbar buttons are almost invisible (only my own styles are affected by that).
http://dmcritchie.mvps.org/firefox/firefox-problems.htm#fx29

Firefox 29.01 Mac OS X 10.9.3 Tabs for some websites (but not all) will not close nor will the site allow me to navigate back to an earlier page (away from the problem site). Unlike that mentioned above, the X on the tab is there but inactive.

This has happened with several sites including one academic journal publisher. The offending site today is space.com. I haven't had a problem with this site in the past but it has been several months since I visited.

I have tried disabling add-ons and after restarting the problem still exists for the problem sites. Is this a programmers way to hold me to a site? This particular (space.com) site now has an auto-play video that will not stop. Last week, the publisher's site no longer had an auto-play video and the tab was able to be closed.

Keyboard commands to close tabs also do not work for problem sites but not all sites.

I initially thought that the problem might be related to the non-closing being the right-most tab but after adding additional tabs is seems that tab position doesn't affect the ability to close.