You probably don't have flash installed, and Firefox doesn't have Media Source Extension support for h264 yet, which YouTube has required for 480 and 1080 video since last October (IIRC). According to this bug, support for MSE h264 will be landing in Firefox 33. https://bugzilla.mozilla.org/show_bug.cgi?id=1027875

The 1080p option isn't shown because YouTube requires Media Source Extentions enabled (HTML5 DRM) for this. You -can- enable this under about:config (media.mediasource.enabled) but it's still experimental for now. When I tried it, it did show the 1080p option, but then I had very mixed results from the blank video, no audio, or the higher resolution video not actually loading.

This should also only apply if you have the HTML5 player enabled on YouTube, the Flash player should still show the 1080p option.

Is that a specific FF issue?

I'm asking because of course some videos do not have a 1080p option in the first place.

What OS are you seeing this on? I'm able to see 1080p on osx mavericks