I look at 404s (and other errors) in prod. Helps find front end bugs and any malicious requests. A 404 should be exceedingly rare in a mature application (depending on the application of course and users' ability to create AND delete data) so it's often a useful metric for figuring out if something's wrong. I don't usually tail the logs and use monitoring instead, but same effect. After a certain scale, I imagine this becomes harder to do and requires different tooling.