The problem I had was that trying to scroll the page using the keyboard resulted in a cursor moving around the document, instead of scrolling the whole page. Believe me, extremely annoying behavior, since it jumped across columns unexpectedly.
My diagnostic was that I had hit some kind of compatibility problem between Epiphany and the version of Mozilla I had installed through the mozilla-gtk2 package. This belief was increased this morning when I noticed that the configuration script was not finding some header files properly. I reviewed it and fixed some problems, but the problem did not disappear.
So this evening, while surfing the net, I thought... let's search for a solution; typed "epiphany scrolling" in Google and... ta-da! There it was, the first match contained what I was looking for, a FAQ about Epiphany. Scrolled down to the eighth question from the sixth section, "Scrolling with the keyboard doesn't work, and instead there's a cursor moving around!", and found the solution.
Copying verbatim: 'You have activated "caret browsing" mode. Disable it with the F7 key.' OMG, OMG! What a stupid "problem" (if I can call it as such)! Pressed F7 and it went away. No comments. Just be aware it doesn't happen to you ;-)