Screen shot taken from modern.ie VM Build number:20150801 running on Parallels Desktop 11.0.1

Thanks, @sathomas, I'll take a look at this.
As a workaround I removed the MDL styling from the sliders on Edge:
$(function() {
var user_agent = navigator.userAgent;
var edge = /(edge)\/((\d+)?[\w\.]+)/i;
if (edge.test(user_agent)) {
$("input.mdl-slider.mdl-js-slider").removeClass("mdl-slider mdl-js-slider");
}
});
Still looks okay, and is a lot more usable until this bug is fixed.
It looks like Edge handles the native styling of sliders differently from IE.
We'll be reimplementing sliders without using native styling in v2, but for now we should add a browser hack to solve this issue in Edge.
What's the status of this? I just noticed this looks bad in Edge on my site so I checked the getmdl page and it's exactly the same. This is almost unusable on Edge, the hit target is tiny.

The Edge solution is to specify the height of the input["range"] element. Since it doesn't depend on the thumb height, the thumb gets clipped.
.mdl-slider {
min-height: 20px;
}
Thanks @mbaileys, that helped. I found that I also needed
.mdl-slider::-ms-thumb {
/* ... extra stuff, height, width etc. */
transform: scale(1) !important;
}
Thanks @mbaileys and @skosch. This was a big help.
Most helpful comment
The Edge solution is to specify the height of the input["range"] element. Since it doesn't depend on the thumb height, the thumb gets clipped.
.mdl-slider {
min-height: 20px;
}