First off, I realize that there are other posts about video problems in Epiphany, but I could not find one describing this exact problem (I also used google to search site:raspberrypi.org in addition to the built-in forum search).
My problem: videos in Epiphany always play through fine the first time. If I let a video play through to completion, and then play it again without refreshing the page, on the second playthrough the framerate is noticeably stuttery (but audio is fine). Is this a known issue, or has anyone else experienced this problem? As a quick test, try the first video in this blog post:
I am running updated (sudo apt-get update && sudo apt-get dist-upgrade) Raspbian on a B+, if that makes a difference.