Here two more suggestions:

1.- I noticed that when I get a new email, this is not shown in the contact feed in the contacts bar. If i receive a mail form someone who is in my contacts bar, it should be shown there too, thing that could be useful for a faster access to the email or threaded email conversations

2.- Every time I received a new mail, is really annoying to open the menu bar, open applications tab, look for the email icon, press it an open my account, all this to see the email that I just received. There must be a way to access it faster, at least, a visual notification like when a new SMS is received, and open it right away.

This kind of applications should be integrated with the phone