Firstfives.org

For intellectual discussion only: As E12's were manufactured beginning around the same time as government bureaucrats were seeking simple solutions to air pollution,...

Loosely in the same book as corn is renewable, for eating or burning. Which makes huge massive corn growing corporations happy to fill in bogs, low lands, estuaries to grow more, and flood more, for ethanol to eat aluminum components in older cars, get half the miles per gallon, in another government monkey drill.

All things considered, as with a 1968 Chevy V8 in excellent running condition, well tuned, (pre cat)...does a 1980 BMW M30 big six run better, cleaner with an O2 sensor and Cat ? Or if they both fell off nobody driving one could tell, and they wouldn't stink up the sky any more than a '92 buick hoopty ?

It is my understanding that the o2 or Lambda sensor is integral to the ecu computing the correct fuel ratio. My 81 sure runs better with a fresh o2 sensor.

Well the gov set the standards they felt the automakers could meet, but didn't care an awful lot if it was easy or hard, simple or complicated. And many of them particularly GM jumped up and down and shouted we can never do that, it's impossible. But they always managed to.

Now take your '80 528i, yes it is cleaner with either the O2 sensor or the cat and still cleaner with both. In an era of low performance and poor driveability it did remarkably well at both. Plus it was clean for the era. Remember California Corvettes of that year were only 180HP, with a big V8.

In California, cars gets smogged and you can see the actual numbers. New stuff has practically no emissions. The old cars were terrible comparatively. Putting aside how the government implements pollution controls, the numbers don't lie.
My 2002 had an M10, 2-liter with a 32-36. It was well maintained, ran very well, produce 100 hp. It would burn a tank of gas at the track in one day.
Then I swapped in an M20. Stock. 168 hp. Lots of fun. A lot faster. Yet, it burned half a tank for the same amount of driving but produce more power, thus using more energy. Half the fuel. And that's an M20 for 1988. I take my S52 powered 318ti, and I burn less fuel than my M20.
Fuel metering, cam timing, precision, temperature control, precise ignition timing, multiple 02 sensors all lead to increased efficiency, and less pollution. Did you see the new N20? 2 liter turbo 4-cylinder, 240 hp, 260 torque, 47 mpg, practically zero emissions. Technology encouraged by regulation.

Sounds like a new cat and sensor is the best solution all around.

Do we just install a new sensor or is there a simple way to test one up to specs ?

O2 sensors have a 50K mile life. If an engine burns oil, it would shorten the life of the sensor, simply because the surface gets coated and the sensor no longer gets proper exposure to the exhaust gases passing through.
They are cheap enough for the E12s.