The Internet has made cheating on papers far easier than it was in the past. You could read this NY Times article about it, if you wanted. My point is less about that there is cheating and more how one could automatically detect it. Right now, it seems like it's ad hoc, relying on the grader's intuition and checks against sources like Wikipedia.
I think that instructors should use statistical analysis of a student's work to come up with a rough model of their writing patterns, including vocabulary, phrases, sentence structure, and the like. Then they should compare the student's work against that corpus. These profiles should be shared across courses and semesters. It would make it much harder to copy other people's work because it would require copying from the same people each time. That's tough to do with an external source, and also tough to do with a classmate, as their profiles would be available for comparison as well. Or the cheat supplier would have to emulate the cheater's profile, which is not easily done. That's still in the realm of possibility, so schools would have to make sure that at least some of the work in the profile was the student's. That would be accomplished by having regular, in-class writing exercises, under supervision, hand-written, and without the aid of computers or the Internet. Those pieces would be scanned in and added to the corpus. Obviously, none of this would make cheating impossible, but it would hopefully make it harder than just doing the right thing.