Firefox becomes very slow and frequently stops responding on sites that have a long scrolling page that continually loads content such as Facebook and Tumblr.
Facebook is home to many unresponsive script errors as well. This is on at least the last few versions of Firefox.
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Since these sites tend to be video-heavy, could you test disabling the protected mode feature of the Flash player plugin. This feature has security benefits, but seems to cause unresponsive script errors on some systems. There is a hidden setting for disabling it:
(A) In a new tab, type or paste about:config in the address bar and press Enter. Click the button promising to be careful.
(B) In the search box above the list, type or paste flash and pause while the list is filtered
(C) Double-click the dom.ipc.plugins.flash.disable-protected-mode preference to switch its value from false to true.
This might not take effect until all Flash has been unloaded for a few minutes, or you close Firefox.