Any thoughts on problems driving (sinking) 4 LEDs on the 5V rail and 4 Relays on the 12V rail with the same ULN2803? (diode clamp on 12V rail)
Since the 5V and 12V supplies go to the same Ground there should be no problem sinking either or both.
Yup, the diodes only needed on the relay windings so that should be fine. Don't forget current-limiting resistors for the LEDs.