Just by way of confirmation: the update to Firefox 26 stopped conkeror from launching with exactly the
same console output provided by quantum.  Installing 'Mozilla XULRunner 26.0 - 20131205075310' seems to
have fixed the problem as well.

Details: 
Ubuntu 12.10, 64 bit

$ firefox -v
Mozilla Firefox 26.0

$ conkeror -v
xulrunner not found, trying firefox instead. 
conkeror.mozdev.org conkeror 1.0pre (Debian-1.0~~pre+git1312212307-~nightly1)

$ conkeror
[output as described by quantum above]

And (now) this works:

$ xulrunner -v
Mozilla XULRunner 26.0 - 20131205075310

$ xulrunner /usr/share/conkeror/application.ini