1. I'd have the browser recommend apps to install to open otherwise unsupported MIMEtypes & URI schemes. I think most desktops support this now (certainly FreeDesktop.Org-compatible Linux & BSD ones do via "AppStream"), it'll free webdevs from compatibility worries, & allow low-cohesian features like videoconferencing & (like brimstedt & osrec discussed) apps to be entirely independant codepaths.
2. For the sake of markettability & accessability (unlikely bedfellows) I like to target unusual human interface devices, e.g. voice, "smart" TVs. It should be a goal to work well absolutely anywhere!
3. I was kind of surprised to find that the next biggest simplification after dropping JavaScript is to move forms out-of-line from the webpage into their own codepaths. This allows me to better reuse OS code whilst simplifying hypertext event handling, avoid webdevs complaining that native widgets clash with their designs, & design a better UX for more devices.
4. There seems to be plenty of precedence suggesting it'd be a good idea to allow links to partially update a webpage, or open modal dialogs/popovers. hey.com is a prominant example.
5. The DOM needs to be replaced, it's an overengineered OO monster straight out of the 90's that can be largely replaced with about 10 lines of code in any language. It's expensive for the browser to construct, for JavaScript to optimize away, and for webdevs to deal with directly.
6. I've got almost no complaint against CSS (I found it easy enough to implement), but sometimes author styles actively make websites worse. So support for user & alternate styles should be emphasized to the user, and websites should still look good if they don't provide CSS.
7. Drop support for CSS `position:`, there's better alternatives now & it does more visual harm than good.
8. I prefer XHTML over HTML as it's easier to parse, but there's a better compromise to be reached between the two camps than the one WHATWG prescribes: handle self-closing tags and close any intermediate tags between the current one & the explicitly closed ones. This routine seems to work well enough on the modern Web, even if it'd break some CSS selectors.
That covers the main points, I'm curious to hear other thoughts?