I've noticed that when I view the page on my phone (it's an iPhone 6), when I try to scroll through the chatbox, it freaks out and shakes around a lot for a few seconds, and then scrolls normally (albeit rather slow). This only happens on my phone; it seems to be fine on both my desktop and my laptop.
I'm using Safari. I also just tried Chrome, and it has the same problem. It doesn't seem to happen every time, only occasionally.
I tried it on an iPhone4/5/5s and an Xperia SP and a Samsung Galaxy Tab 4.7.0 none had this issue. the only issue I can think is a slight delay in loading the Javascript/jQuery which adds a slight jump.
Just tried on an iPad. Works fine. Tried my crappy 2nd generation iPod, too - it took about a minute to load the page and would have blank sections for a few seconds (I guess low RAM), but was fine once loaded.