The Github gists feature is interesting to me because it provides a facility to publish things that are of interest but may not rate a new repo, like snippets of useful code. I would like to follow a user's gists and know when a new gist is published, but I see no way to do that in the web user interface. Is this possible?
Yes, this can be done, but you have to use the combination of the Github Gist API and a bit of coding. One example of how to do this is here, using Python. This utility lets you query a Github user's gists, and creates a small file with the timestamp of the latest gist. When you run the query again it checks to see if there are any newer gists and lets you know, then updates the file with the new timestamp.