2002 BMW 530i service engine light on

It could be any number of things you will nee the codes read to be sure. If yor mileage is near one of the recommended services points 50,000, 100,000 or 150,000 this could be the cause. Again you won't know or sure ill codes are read Good Luck With This

How do tell if the O2 sensor went bad?

Go to your local auto parts (most would scanned and give you a printout with the codes that are faulty, per example ph345 is the camshaft positioning sensor bank 1 intake side, after the sensor is replace ,check engine light will stay on until you drive a 21 miles + _ couple miles cycle, the light should go out by-itself, no need to take inn the shop so they can turn it off, if you fix the problem the check eng light should complete its diagnostic cycle and the ecm will compensate like it did when it register the faulty sensor..