Just to make sure that an extension isn't causing this issue:

Start Firefox in Safe Mode to check if one of the extensions (Firefox/Firefox/Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox/Firefox/Tools > Add-ons > Appearance).

• Do NOT click the Reset button on the Safe Mode start window.

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

I've tested it in Safe Mode and the issue remains. Please see for yourself by visiting for example https://plus.google.com/105658931286740311674/about.

Yes, I see that too on the page that you supplied.
It look that some script is running and is used to cycle between a few possible pages.
Ctrl + Page Up and Ctrl+ Page Down work after I press the F6 to move focus away from the page or otherwise remove the focus.

Is there a script running or is it a hypothesis? Can script do that? I mean catch hotkeys that are used by the browser?

Anyway, back to my question, what can I do about it?

BWT: It works fine in Chrome 30.

Since a recent Firefox upgrade I have the same issue randomly when the focus is on a text input box or field.

For example, this happens on linguee.com on a results page, for example:

http://www.linguee.com/english-french/search?source=auto&query=firetruck

Ctrl + PgUp/PgDn doesn't work to switch tabs, only Shift + Tab does. However, things work fine on WordReference.com.

I use both WordReference and Linguee as tools for my translation work, and I always have one tab of each opened. I switch between them very often, and I'm used to the Ctrl + PgUp/PgDn to do that. Now I get stuck on Linguee all the time. If I use tab or any other means to remove focus from the search text box, the shortcut works again.

Another example of this is Gmail. If I'm composing a reply and the text input box has focus, the Ctrl + PgUp/PgDn shortcuts don't work. If anything else has focus on Gmail (including other text input fields and boxes, such a composing an email, searching, or chatting with contacts), the shortcuts work fine.

I just tried Safe Mode, and nothing changed.

I've made a small addon to fix this issue:

https://addons.mozilla.org/en-US/firefox/addon/free-control/

I hope it help you guys :)