The save dialog being fullscreen is by design.  It is so space inefficient it would end up being too small to be usable on many occasions and it is something that would be up for short periods of time when it is expected it would have your complete attention anyway.

I have not been able to reproduce the problem with the mail app reverting to fullscreen after this (were you trying to use the hotkey to switch modes when the save dialog was open?), but I will pass it over to QA to see if they can reproduce it.