Thanks VERY MUCH for everyone's help - I appreciate it. Forgive me for not having the brains to check iDrive - it's my first E9x M3 (I had 3 E46 M3s) so it didn't even occur to me to check iDrive, which is ridiculous.
Anyhow, I checked iDrive and here's what it said (I am paraphrasing):
"Service Due Soon. 600 miles until oil change. Please make an appointment with a service advisor."
So it looks like I am currently due at around 900 miles. All other systems looked ok. So my conclusion at the moment (unless something changes) is that I will ignore the service mention every time I start the car and take it in when the countdown is close to 0 (probably within 100 miles).
I'm not at all surprised that my countdown is running very early, as I literally drive the car to lunch and back to my home office almost every day. And lunch is usually the Quiznos in Santa Monica that is literally within walking distance of me. In fact, my trips are so short that my oil reading pretty much never shows because I don't drive long enough for a reading...
Anyhow, thanks for everyone's help. I think my case is closed for the moment