I have had this problem with Firefox too, where opening a new window and closing Firefox solved the issue.
With Mail, the app opens but goes in an unassigned part of the screen. Impossible to get it back so far on the main screen estate, it goes on the left (could get a double arrow cursor and replace it on the visible screen estate), but problem has deeper root, as follows..
I thus noticed there is a virtual display on the left part of the screen by default, the mouse pointer can go venture into that screen estate as if there was a second screen; but when I open System Settings and try to open Displays, the window fades to the background and disappears.
Machine is MBP 6,1 with NVIDIA GeForce GT 330M