What I would like is to have lists of questions that only lists the questions that have one or more of my favourite tags attached, so that I can have a quick view of newest or featured questions in any of my favourite fields.
You can create and bookmark a URL of the form
You can use the featured and other sub-tabs to customize the view further.
If you have only a few favorite tags, the above is equivalent to searching for
[tag1] or [tag2] or [tag3] or [tag4]
If you have many favorite tags, they may not fit into the search box (which takes only 240 characters), but you can use a text editor to create the URL as above.