There's a number of reasons for those codes, I'll quote from the service manual directly so I get it right - because despite having been a petrol-head for 30 years, I'm well and truly a diesel guy now!
0420 indicates a measurement problem with the air flow sensor against the heated oxygen sensor in the exhaust. This might be a faulty sensor, or even a loose or dirty connection on the sensors, but may also be a leaking air intake (so it's drawing air from somewhere between the air flow sensor and the intake manifold). Could be a dirty/faulty spark plug, or poor ignition timing, which by extension might also be a bad HT lead. It might also be a poor condition fuel injector. Liqui-Moly Injector Cleaner is awesome stuff and worth a try.
1278/1288/1289 are all bank 1/bank2 air/fuel ratio sensors. Again, possibly an intake air leak, but also might be a dirty MAFS. Remove it, spray the opening with electrical contact cleaner and avoid dropping it or inserting anything into the opening - it's extremely fragile and worth $400. Other possibilities are exhaust gas leaks, lack of fuel (possibly a crushed fuel line, or dirty filter) or the PCV hose incorrectly fitted.
Hope something in there helps. Easiest to do: MAFS cleaning. Use electrical contact cleaner or MAFS cleaner (any reasonable auto parts outlet should supply, or even Jaycar).