First, I DO NOT have a check engine light or any stored fault code.

I just bought a used 2010 Mini Cooper -- base model, standard transmission. After running the car for several hundred miles and refilling the tank in two increments (wanted to give it a chance to run several full EVAP system checks), I plugged in my OBD reader and fired up my Torque Pro app and ran complete tests. Again, no CHECK ENGINE LIGHT and the Torque OBD test showed no stored fault codes.

However, after running a full series of tests in which almost everything passed, I got the following problems/fails:

1. MID:$3d TID $81. -EVAP Monitor (0.020") Test incomplete or dependent test failed.
2. MID:$3d TID:$84 - EVAP Monitor (0.020") Max: 32,767 Min: 98 Test result value 109 PASS
3. MID:$71 TID:$7f-Secondary Air Monitor 1 Max: 2 Min 8,273 Test result value: 32,624 FAIL
4. MID$82 TID:$66 - Fuel System Monitor Band 2 Max: 204.7999A Min: 62.16A Test result value: 656.20001A Fail

Based on these readings, can anybody make any diagnostic guesses? I eyeballed the gas cap gasket and it looks just fine, and I was careful when removing and reinstallling it a few times. I re-did the tests after driving another 20 miles or so and got the very same results.

 

Well, looking at the system, you got a secondary Air Monitor fault. Do you hear the secondary pump kicking in? If so are all of the hoses properly attached. It seems odd that you would get failures for your test, but no faults or check engine lights. It might just be that your Torque pro doesn't read correctly. BMW has some finicky software.

If it were your gas cap you would be seeing a gross system leak P0442 or a small leak P0456 if it was just a sealing problem. Also, this could be a bad sensor on the tank (this detects if its leaking by looking at the tank pressure). Leaks can also be in the purge system or charcoal system.

If you don't have any solid P-Codes or any check engine lights, I would just disregard and chock it up to Torque pro being off.

 

As above! Don't look for problems from a phone app. If you do have an original gas cap, $21 replacement at this point is a proactive cheap thing to replace anyway. It got rid of my check engine light.