What is the purpose of the specimen sheet? Is that the same thing as a demo? It looks like a huge typographical mess to me http://devinhunt.github.io/typebase.css/demo/specimen.html, but maybe it has another technical purpose?
Many head sizes are smaller than main text.
Heads do not sit with the paragraphs they belong to but float in a huge canyons of space - this is basic typography.
Heads mix fonts in the same heading - OK for raygun maybe, not ok for normal use.
Text cols overlap at many widths, and main text is allowed to be too short and too wide.
There's a grid, but nothing sits on it or relates to it (baseline, x-height, cap-height etc). If a grid is shown it should be a baseline grid, and text should be locked to it at least in some cases, somewhere on the page. Looks like the grid is off.
The blurb talks about 'vertical rhythm', but the styles don't display this - instead the two columns are unrelated and jarring - the only thing aligning is the main copy, but that means of course that heads have those awful gaps above and below - a nasty tradeoff which isn't worth it.