So far, it's Safari, TextEdit and Notes that do not open up at all in their assigned desktops. Their indicator lights in the dock show they are running just not visible. Once I click them on the dock they open in their proper desktop.
Apps like Calendar, messages, mail and reminders appear correctly in the desktops I've assigned them right after a reboot.
These apps are not set up as full screen... and I've selected "do not" reopen windows when logging back in.
My goal is to be presented with a fresh set of desktops each one containing their assigned apps ready to go every time I log back in or reboot. Instead the desktops for some apps are blank. This has been going on since 10.8.0 and nothing has changed.
I suppose I'll have to whip up a script to do what Apple can't.