I have several Kubuntu systems, configured the same way, where I have enabled the compose key (I write in multiple languages), but the upgrade to 15.10 on one of those systems broke my compose key.
Specifically it still works in Firefox, Thunderbird (but sometimes with a lag, if I type too fast it won't work).
It doesn't work in Kate, Konsole, OpenOffice, Dolphin, System Monitor... Specifically if I try to compose 2 characters, it will sometimes display both and sometimes swallow the 1st one, never composing them.
I finally found the solution after much searching. I had a ~/.XCompose which probably had a syntax error in it. I removed the file and it started working again.