I don't know what subject or grade level you teach, but I teach high school English. In my class, I have students write their essays on computer (google docs), share with two or three classmates, have those classmates suggest editing, and sign off on it, then hand it in to me when it is more complete, with fewer errors. I'm pretty good at editing, and don't need the practice; they do. :)
In the area of self-assessment, I give an essay checklist, and have them write the letter of the alphabet (from the checklist) on their essays. If they can't find a thesis statement, that is a clue to them that they need one.
I'm not familiar with O'Connor's work, but I've done research using dictoglosses, and they offer a way for teachers to conduct formative assessments based on self and peer assessment.