I'm currently debugging your new design. One problem I discovered first is the lesson navigation. On my browser (chrome) the "review" is not on the same row as "introduction" and "lesson materials" but beneath. Together with the fixed height of .ill-lesson-nav, this creates a rather ugly effect.
The problem is the width of .ill-tab. 33% percent looks quite reasonable at first. This is a common mistake. Between the elements there is usual a distance, so that 3 times 33% plus this distance is more than 100%. I reduced the width to 30% and now all three elements are well aligned.
BTW, I really miss the popup audio.