It'd be very helpful for rapid troubleshooting if you could go to a URL like:
http://example.com/jenkins/job/somejob/latest/console

Where it'd show you the latest console.

It should not redirect, since it would be nice to just press refresh after kicking off a new build to get the latest console.

Ideally, it would just know a new build has started and reload the page itself similar to how it shows the log updating in real-time.