I take it for granted that electronic homework systems cannot effectively grade any math problem that requires students to write coherent sentences.
All the electronic homework systems allow the possibility of students submitting answers that won't be machine graded. This capability greatly increases the variety of types of questions that can appear in an electronic exercise set. There is an issue of how students enter math notation and figures (hey, just let them photograph their handwritten answers with their cellphones and upload the jpg file), but the principal reason that I'm reluctant to include such problems is the fear that grading online will be cumbersome.
There are several ways to make life easier for the instructor faced with grading a single "essay" problem from a large set of students. First, the interface for viewing individual responses should be intuitive and effortless. Don't make us click on a link to open one student's response and then have to close that file before opening the next.
It would be better to have "zoomable" thumbnails of each student's answers spread across the screen, with mouse flicks or dragging to scroll. Should the instructor have the foresight to provide a grading rubric for the problem, that rubric should be visible (or at least available) to the student when working the problem.
In many cases, the availability of the rubric could reduce the instructor's need for to make copious comments. For further convenience, the instructor should have a few editable paste buffers holding common comments (like "You need the product rule" or "This is not an equation").
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The open-source online homework system WAMAP (wamap.org) has just introduced a rubric feature.
The feature is for the exercise that is open-ended and not machine-gradable. The students can see the rubric to be reminded of what they should address, and the instructor has access to a number of customizable comments to select for feedback to the student--just click to select the comment you would normally have to write on multiple papers.
Instructors can provide a rubric for any individual problem, either accepting a generic rubric or customizing each exercise's rubric to the taste of the instructor.
Here's a video David Lippman made to show what it's about: http://www.screencast.com/t/gyGETBpGGm
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