Using YouTube videos for teaching

I was recently asked to clarify the copyright considerations when reusing videos from YouTube for teaching. There are a number of issues to examine:

• Anyone can upload a YouTube video, but does that person own the copyright? We can’t assume they do and we should consider this.
• Maybe the person who posted the video does own the copyright, but have they included any other copyright protected works (music, recent artworks etc.). Does it look as though it is infringing?
• Many YouTube videos have a Creative Commons licence attached which allows reuse in many contexts. So once we have clambered over the initial hurdle of copyright ownership, any videos with a CC licence are potentially reusable for teaching purposes as long as we adhere to the licence terms.
• YouTube has its  own detailed terms of service which appear to restrict the user to “personal, non-commercial” use. On the face of it this clashes with the rights granted by CC licences.
• On the other hand YouTube clearly recognises that copyright is owned by the author of the video, so perhaps we can assume that the CC licence chosen by the author  overrides the general YouTube terms of service?