only one firefox window is responsive

What is the output of:

apt-cache policy firefox; lsb_release -a

Thanks

*apt-cache policy firefox:*
firefox:
  Instalita: 40.0+build4-0ubuntu0.15.04.4
  Kandidato: 40.0+build4-0ubuntu0.15.04.4
  Versionstabelle:
 *** 40.0+build4-0ubuntu0.15.04.4 0
        500 http://de.archive.ubuntu.com/ubuntu/ vivid-updates/main amd64 Packages
        500 http://security.ubuntu.com/ubuntu/ vivid-security/main amd64 Packages
        100 /var/lib/dpkg/status
        37.0+build2-0ubuntu1 0
        500 http://de.archive.ubuntu.com/ubuntu/ vivid/main amd64 Packages
----
*lsb_release -a:*
LSB Version:
core-2.0-amd64:core-2.0-noarch:core-3.0-amd64:core-3.0-noarch:
core-3.1-amd64:core-3.1-noarch:core-3.2-amd64:core-3.2-noarch:
core-4.0-amd64:core-4.0-noarch:core-4.1-amd64:core-4.1-noarch:
cxx-3.0-amd64:cxx-3.0-noarch:cxx-3.1-amd64:
cxx-3.1-noarch:cxx-3.2-amd64:cxx-3.2-noarch:
cxx-4.0-amd64:cxx-4.0-noarch:cxx-4.1-amd64:
cxx-4.1-noarch:desktop-3.1-amd64:desktop-3.1-noarch:
desktop-3.2-amd64:desktop-3.2-noarch:
desktop-4.0-amd64:desktop-4.0-noarch:
desktop-4.1-amd64:desktop-4.1-noarch:
graphics-2.0-amd64:graphics-2.0-noarch:
graphics-3.0-amd64:graphics-3.0-noarch:
graphics-3.1-amd64:graphics-3.1-noarch:
graphics-3.2-amd64:graphics-3.2-noarch:
graphics-4.0-amd64:graphics-4.0-noarch:
graphics-4.1-amd64:graphics-4.1-noarch:
languages-3.2-amd64:languages-3.2-noarch:
languages-4.0-amd64:languages-4.0-noarch:
languages-4.1-amd64:languages-4.1-noarch:
multimedia-3.2-amd64:multimedia-3.2-noarch:
multimedia-4.0-amd64:multimedia-4.0-noarch:
multimedia-4.1-amd64:multimedia-4.1-noarch:
printing-3.2-amd64:printing-3.2-noarch:
printing-4.0-amd64:printing-4.0-noarch:
printing-4.1-amd64:printing-4.1-noarch:
qt4-3.1-amd64:qt4-3.1-noarch:
security-4.0-amd64:
security-4.0-noarch:
security-4.1-amd64:
security-4.1-noarch
Distributor ID: Ubuntu
Description: Ubuntu 15.04
Release: 15.04
Codename: vivid

Is it the same in Chrome?

So far I hadn't installed Chrome, and as I have no fully dependable way of reproducing the phenomenon it's not easy to answer your question.

I just installed Chromium, which is I understand a sibling or parent project to Chrome, and I tried what I sometimes did when Firefox showed the problem: Watch a news video in one window and edit text in another. But Chromium just showed me snow instead of the video. So I haven't any clues to your question so far.

Does it work as desired, if you temporarily disable all add-ons in Firefox?

Good idea to disable the add-ons. I did that, and today the problem reappeared twice (I closed the second window after the first time, opened a new one, and a bit later had the old problem). I checked the add-on list and found that for some reason two add-ons were still active or active again, maybe due to a system update: "Ubuntu Modifications" and "Ubuntu Online Accounts". I have now deactivated these, too.

I noticed that sometimes when I respond to an e-mail message in Thunderbird (which is Mozilla, too) the keyboard focus won't appear in the response window until I close the original message window. Maybe that is a related phenomenon?

Today the phenomenon occurred several times, and all add-ons are securely deactivated (two reboots since then). It just now happened that I had two FF windows open, both active, and when I opened an additional tab in window A the keyboard focus jumped to window B and would not return to A until I closed B.
I still have no way to reproduce the phenomenon in a reliable manner.
Unsually when I have to FF windows open one is on the notebook screen and the other on an external screen; I have no idea if that could make any difference.

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