You do need to make sure both player and receiver have up-to-date firmware. You can download firmware for the Oppo, but not for the Marantz -- that has to be sent to a repair center.
There has been at least one firmware update for the NR1501 since it came out. I don't know if it'll fix your 83's CD audio problem, though, and I don't know of a way to find out what the AVR's actual firmware version number is.
However, a bug that I do know that the NR1501 firmware update fixes is a 1/4 second (or so) audio dropout that happens when using a BD player and HDMI connections. The dropout is "heard" at the start of the next DVD chapter or CD track when you use the "advance" (>>|) button to skip to the next chapter of a DVD or the next track of a CD. Typically several measures will be missed from the sound at the start of the skipped-to CD track. This bug is actually described as a "feature" in the NR1501's manual, but they'll fix it if you complain.
My NR1501 had this bug and it was fixed by getting the firmware updated. It took several weeks, though, because my NR1501 was the first the regional repair center had received for an update and they had to get the necessary firmware reprogramming hardware from Marantz. If you're lucky, your local repair center may already have it.