A simple linux distribution as a base (as with Android), with posix. They could still lock-down app installation for normal users, have an app store, and all the other things that make current mobile platforms attractive to consumers.
Hooks for any popular languages to control the UI via simple glue libraries, all implementing the same API, with the ability to add more easily because the UI API could be really quite simple (and should remain so) if built off the work already done for the web. They could add C, C++, Golang, Java, C#, even ObjC to the mix this way. There's no chance they'll do this for their current API, so they'd need to have a radical rethink of just what a mobile OS should provide.
A web-based stack for the UI based on an improved webkit (a la webOS). Most apps have very simple needs (specify a UI, adjust the UI, listen for UI events) that could easily be dealt with by message passing between the view and app rather than binary interfaces. Webgl and css animations etc could be utilised for performance where required. Crucially this wouldn't tie developers into one complete stack from language to tools to UI - the UI should be separate and not tied intimately to the back-end language as it is currently on iOS and Android.
A base OS that is non-negotiable and non-modifiable by carriers/manufacturers, and upgrades from a central point (a consortium led by Google), that are not phone-specific. Carriers can add apps etc but there's no reason they have to adjust the base OS, and both should negotiate with Google for inclusion of new drivers, not hold up upgrades because they want to sell newer hardware/contracts.
Far stricter permissions for apps with far less access (more like web-apps), and individual prompts on first use of info like phone no, addresses etc. to discourage overuse.
It's a shame that our mobile devices are typically tied to one platform, one language, one UI, when they have so much potential as portable computing devices.