P0420 is as follows: The catalytic converter has an oxygen sensor in front and behind it. When the vehicle is warm and running in closed loop mode, the upstream oxygen sensor waveform reading should fluctuate. The downstream O2 sensor reading should be fairly steady. Typically the P0420 code triggers the Check Engine Light if the readings of the two sensors are similar. This is indicative of (among other things) a converter that is not working as efficiently as it should be (according to specs). It is part of the vehicle emissions system.
P1705 Automatic Transaxle Concerns