I personally don't like the idea of reusing courses (deleting students and then adding new students). It leaves you without a record of the previous semester, and there have been some minor complications with old answers appearing for students who re-take the course.
You can easily create a new course with the same problems/homework sets: First, in the old course, export all of the homework sets from the Homework Sets Editor. Now log in to the admin course, and create your new course. While doing so, set "Copy templates from:" to the corresponding completed course. When you log in to the new course, you can then import multiple sets using the Homework Sets Editor. You can even have it shift the dates to match the new term.