From a philosophical point of view, I don't think chemistry problem sets should be submitted online. Often the submissions end up being answers to multiple choice questions. However, chemistry problems often involve calculation and this work cannot be submitted in an online format. Thus, the online homeworks tend to place too much of an emphasis on the answer and no emphasis on the work leading up to the answer, whereas the actual work and calculations are the important part of the problem. Paper problem sets also offer TAs the opportunity to correct mistakes in a students' logic (e.g. showing which steps are wrong in a calculation) and offer feedback whereas multiple choice online quizzes exclude this option (of course, this presumes the TAs are motivated enough to grade the homeworks carefully).
The one somewhat effective use I've seen, however, is a system called Calibrated Peer Review (CPR) where students answer a prompt in essay format (for example, explaining how to analyze a spectrum or explaining how to perform an experiment). The system then allows students to anonymously grade each other, following questions and guidelines created by the instructor. Sometimes this leads to some interesting game theory (you are penalized if your evaluation of an essay deviates significantly from the average evaluation of that essay), but I like the system because it gives students experience in critically evaluating the work of others as well as allowing students to obtain feedback on their own work.