I suppose the most obvious problem with Internet-based classes is security. Even more recently, Presidential Candidate George W. Bush's web site was cracked and totally altered, littered with Communist propaganda. We may think that we're safe at Wabash, but no one really ever is. Just because we've never been the victims of such activities, we shouldn't get complacent. It could happen.
Some people see anonymity as one of the greatest benefits of the Internet.
Some, like myself, can see it as a problem as well. You can represent yourself as anything you want on the Internet. Herein lies another problem to the Internet based classes. When I go to my Inorganic Chemistry class, for instance, I know that I am being taught by Dr. David Phillips. I know who he is and above all else, I know that he knows what he's talking about.