Rather than re-clicking questions, is there an option to refresh the list automatically as new ones come in?
Elsewhere on the site there is at least a notification when new comments come in or changes are made.
It looks like with the new site layout, this has been implemented. When I have a tab with a couple favourite tags selected, the browser title shows the new questions, as well as the tab, like so:
And if I'm sitting on that tab, it shows the number of new questions waiting to be viewed now, and I can just click it to reload: