All of the fixes people have posted here turn out to be temporary or not at all - eg. changing click speed, getting rid of Emoji, turning off mobile data, restoring factory settings, setting up as new, etc, etc, etc. Sometimes I think the problem has gone but that's just because of its intermittent nature. It always comes back, so I think people are wasting their time trying to fix it. I know people are trying to help and they mean well, but I've come to expect that the latest fix will not work.
There is probably a hardware element to the fault and for some reason ios8 sometimes thinks it received one two or three clicks - but who knows?
Two things seems certain - one is that relatively few devices are afflicted by this bug. The other is that, due to the low incidence of this problem, it is a very low priority - or a non-priority - for Apple.
I suspect that the only solution for those of us who have this bug will be to buy a new phone. Mine will not be an iPhone, but I don't think anyone over at Apple will lose a lot of sleep over that.