Most important by far - network reliability. There was THE INCIDENT last fall where nothing was working, which got fixed, but almost daily at least one student is having network response issues. I don't know if you could deploy a proxy server on site or something like that, but my kids do get frustrated watching the little circle spin, and frustrated children are not a good thing ...
Other requests in no particular order:
Save Defaults. I always want my gradebook scaled by difficulty, and my quizzes as raw score, but I have to set that every time.
Save context. stryba mentioned above that it would be great to switch students and keep the current exercise. Extend that to across sections as well. If I bounce around looking at student's work, I more often want to keep most context the same rather than starting over.
Include test and quiz scores into the gradebook. I record 3 scores from each module - assignments, total quiz score and test score. If I can open the gradebook and see all three that would make life much easier.
Screen real estate. The squished image posted by cdonaldson above occurs far too easily. CodeHS assumes a certain screen size - if that changes things break loose pretty quickly. I'm fortunate enough to have a 1920x1080 monitor on my desktop, and for most applications I do 2 side by side windows. CodeHS does not work well in that scenario. The navigation panel on the left side appears not to be resizeable or hideable, and other items either wrap or smoosh to make up for it. Using it on my Jurassic laptop is also a challenge.
That's what comes to mind now - if there's more I'll certainly let you know