For the vast majority of the people on the planet, GMail is just good enough. Yahoo Mail and Hotmail are still doing well.

Perhaps email is perceived as a problem just because it gets tons of "face time" with us every day. I'd leave it alone and focus on one of the countless unsolved problems in the world.

It is, but only in terms of what we think of email in today's usage. I think the next step will be where you can make the messages dynamic which would basically allow you to receive/deliver an interface to an app. Of course with all that power comes the issue of how to control it, but that would be an interesting problem to solve. Imagine instead of getting a notification email for an update on a Basecamp todo list, you would see the actual todo list and could manage right from your inbox.

Emails can send HTML and JS, there's nothing innovative about it. You only need to convince developers to add JavaScript sandboxes to their email clients.