I propose to make it possible for MediaWiki to put a (1) in the browser tab to indicate there is a new recent change (or other notification) on the wiki. This would be similar to what Facebook, Quora, Gmail, etc. do.
An alternative idea is T1188: Include echo notification count as a favicon badge
The discussion in comments below, suggests that that this should be an opt-in gadget/userscript, and not a default feature.