This is a great idea. I actively encourage my students to video parts of lessons, demonstrations etc., with the understanding that it is for their use only. I often video them playing once they have mastered the correct technique. My students often find this more helpful since they can remember how it felt to play that technique as they watch. They play slowly using the techniques to see them broken down.
I sometimes make videos of myself or students playing and slow the video down using quicktime or similar to enable them to break a technique down and see how it works on a micro level. I also encourage students to make use of mobile phones for videoing short sections when practising. The quality isn't great - but it is easy to put the mobile at either end of the keyboard and record. Students are constantly surprised at how this simple technique can inform them about their technique and habits when playing.
The thing to watch out for is that you are not listening or concentrating properly in the lesson because you think you will be watching the video back later. It is a
supporting technique, not something to replace concentrating hard in the lesson.
I understand some teachers are cautious about having students video them - but I think as long as the student understands it is only for personal use you should be fine. I have my students and parents sign an agreement before starting lessons detailing things like this and (half) jokingly tell my students I will sue them and retire if they post anything without my permission!
