As promised, here are the instructions on how to get to the "Test Modes" of the OBC. I didn't run into any trouble, but as always, do this at your own risk

BMW apparently doesn't want you to play with this, so most modes are locked. Once you unlock them, they remain unlocked, until you bring in your car for service, or explicitly lock them yourself.
UNLOCK PROCEDURE:
1) Key to ignition pos 2 (no need to start engine).
2) Fasten the seat belt to get rid of the "Fasten Seat Belt" message.
3) Press the right button on the instrument panel, and hold it until "TEST-NR. 01" comes up (5 to 10 seconds).
4) Press the left button on the instrument panel, and the vehicle id comes up (last 7 digits of VIN).
5) Add up the last 5 digits to get the "unlock code", e.g. the unlock code for "AB12345" would be 15 (1+2+3+4+5).
6) Repeatedly press the right button until "TEST-NR. 19" appears.
7) Press left button -> "LOCK : ON"
8) Repeatedly press left button until "LOCK : xx" appears, where "xx" is your unlock code.
9. Press the right button. All modes are unlocked now.
NAVIGATING BETWEEN TESTS AND PERFORMING THEM:
- Follow steps 1) to 3) of the "UNLOCK PROCEDURE" to enter test mode.
- Use the right button to step from test to test.
- Press the left button to enter a test and cycle between modes within a test.
- Press and hold the right button to exit test mode (turning the key to 0 works as well).
Here is what I know about the various test modes:
2) Instrument test: Cute light show in the instrument panel. Ever wanted to see the speedo show 190 without having to leave the garage?
3) Don't know.
4) Current fuel consumption in liters per 100 kilometers and in liters per hour.
5) Average fuel consumption in liters per 100 kilometers and range.
6) Current fuel levels in left tank, right tank, and total.
7) Engine temperature (not sure where measured), engine RPM, and outside temperature.
8) Current speed in kilometers per hour.
9) Battery voltage.
10) Country.
11) Don't know.
12) Not sure what these are. Could be average speed used to calculate arrival time for distance to destination set in OBC?
13) Sound test. Goes through the various gong sounds.
14) Don't know. Could be some diagnostic codes.
15) DOn't know. Looks like a real-time readout of some registers.
16) Oil temperature. I sometimes get a bogus -48 degrees C when the engine is not running. Corrects itself when the engine is on.
17) Don't know.
18) Doesn't do anything.
19) Locking & unlocking of the test modes.
20) Don't know.
21) Don't know. This test asks you "RESET?". Let me know what it does, if you're brave enough to try it. I'd recommend to stay clear, though.