OBD-II trouble code P0420 is a common BMW trouble code and indicates a possible fault with the catalytic converter. The actual description for trouble code P0420 is "Catalyst System Low Efficiency". With a P0420 it is very important to properly diagnosis your BMW 328i's entire emissions system. P0420 may be a false code if other emission problems exists; particularly, a incorrect air/fuel ratio.
P0420 basically says something is wrong with the CAT, however, it bases test results on how well the CAT reduces emissions. Using the front oxygen sensor your BMW's engine control unit (ECU) takes an oxygen reading before the CAT, and using the rear oxygen sensor, a reading after the CAT. If the ECU senses that the reduction in CO after the CAT is not significant, it triggers a P0420 fault; saying the CAT is not doing its job. What we have to keep in mind though, is that in order for the CAT to work properly, air/fuel mixture must be precisely adjusted to 14.7/1. So any fault which could alter air/fuel mixture can potentially cause a P0420 trouble code fault. It is not recommend to suspect a bad catalytic converter until the rest of the emission system(s) have been diagnosed for proper operation.
We recommend checking your BMW's front and rear oxygen sensors; using a professional multimeter preferably one that will show wave patterns. When doing this test while your BMW is warm and running in closed loop mode, the oxygen sensor waveform reading before the catalytic converter should fluctuate. The O2 sensor waveform reading AFTER the catalytic converter should be fairly steady, anywhere between .15 to .45 volts. If the rear O2 sensor has no reading, replace the sensor. If the voltage reading is above .45, the CAT is not able to reduce emissions efficiently. After ensuring proper air/fuel ratio and correct functioning of other emission related systems, suspect a defective catalytic converter.
Trouble code P0455 indicates an EVAP emission control system leak (large); more than likely a broken or disconnected EVAP hose. The fix here requires tracing all the EVAP vacuum hoses from the engine to the charcoal canister to the gas tank, including inspecting the vent and purge solenoids. Inspect all the EVAP hoses, as mentioned above. Look for breaks, cracks, and disconnected lines. Check for the proper operation of the EVAP purge solenoid. The EVAP purge solenoid will be located near the charcoal canister and allows for gas tank fumes to enter the intake manifold when activated. If no faults have be found with any of the EVAP hoses and/or solenoids, you should inspect the EVAP canister itself.