I'd like to link to a YouTube video from my course website on Brightspace. What are the copyright implications, if any?

Linking to web content for use in a face-to-face classroom setting for the purposes of teaching and learning is generally fine. However, if you link to infringing material, it could be labeled with a takedown notice and removed suddenly from YouTube without warning. If you suspect material may infringe copyright law, you should make every effort to locate an alternative source. Ask a Librarian about locating a licensed version of he film.