There's been a bug going back to early 2002 about properly integrating Mozilla with KDE, "Mozilla has 'Windows Integration' on win32, I believe it should have such a thing on KDE as well (gnome folks, feel free to file your own bug). We should at least provide an icon in the KDE menu, perhaps we could even tell KDE that some file types can be opened with Mozilla..." That bug, Mozilla Bug 140751, has been open for the past twelve years and finally now might be inching closer to being resolved.
A Phoronix reader pointed out this comment yesterday with trying to spearhead new efforts to improve the KDE + Firefox integration and getting Firefox to use KDE's Dolphin file manager.
While there's been many out-of-tree patches out there for improving Firefox on KDE, they haven't been mainlined. Grant K, who is organizing these new efforts, wrote, "As of this date, there's still no solution that works consistently well. Opensuse's patches are the closest to it (cref packages: 'kmozillahelper', 'mozilla-kde4-integration'), & have been intermittently available/functional in Opensuse, as well as ported to Ubuntu, Arch, others. But, even the Opensuse devs say they're not happy with their own, 'hacky' solution. And, unless I've missed it, the 'right people' simply aren't talking to one another."
There's also this mailing list thread discussing the Firefox + KDE support.
While some are hopeful that the KDE support will finally improve, Justin Dolske of Mozilla was quick to remind everyone that while there's many KDE Linux users, overall the number is very small. Dolske responded, "Keep in mind this is is a very relative number -- _All_ Linux usage represents about 3% of Firefox usage. We have 7x more _Windows XP_ users...KDE support hasn't been a priority for Mozilla, nor is it currently a priority. Getting better support for KDE into Firefox will need to be an effort driven and sustained by the KDE community."
Richard Newman of Mozilla also argued, "Mozilla isn't a company that's trying to win the market. It's a community that's trying to change the world. That MoCo doesn't fund the salaries for development of Thunderbird doesn't mean it's abandoned, and that people use Chrome doesn't mean we've failed -- quite the opposite! Chrome is a great browser. A rising tide lifts all ships."
Mozilla seems to be under the position of willing to review patches and mentor new developers, but that the initial integration work will need to be proposed by KDE developers. In the mentioned mailing list thread there's some willing to step up to revive the KDE Firefox patches, so we'll see in the weeks and months ahead if these efforts prevail and are sustainable in seeing the Firefox support improve for the KDE desktop.