The Nature of Writing is a resource created by Conrad van Dyk, medievalist and linguist at Concordia University. It offers smart video lessons, exercises, and other information on grammar, mechanics, citation practices, and basic aspects of rhetoric. Students can learn a great deal not only about “the basics,” but also central principles about how language functions. Highly recommended.
The most recent major study of student error in first-year writing was conducted some time ago, but its general findings still hold.