First, the exchange/calendar integration options clearly suck... establishing a clear calendar interface as a built-in with extensible points for plugins for authentication/sync of calendars would be a good start.
Second, likewise with calendar auth/sync would be an extensible interface for folder sync and authentication, so that a cleaner integration for common providers based on an underlying IMAP can be used... this way the conventional "junk, spam, inbox, sent" folders could be presented the correct way as well as the underlying storage for a given provider.
Also, along with calendar/email would be more extension points for scheduling, contacts, etc...
As it stands, even if there were different plugins for a google calendar and an exchange/o365 calendar, contacts, etc... if the underlying pieces can be shared, it would be a better user experience.
Moreover would be some serious reconsideration regarding the UI/UX... I'm a big fan of material design, but some variation on that coming a lot closer to a Gmail app for desktop would be a really nice start... but getting a calendar/task/contacts integration points and primitives for extension would go a long way here. Having the core UI going the same direction as Servo, and having most of the UI/Extensions being HTML/JS based would be nice.
Likewise, NPM compatibility for extensions' modules would be nice as well.