Nissan Pathfinder odometer/ABS/speed sensor problems

ABS/VDS started behaving funny and then turned off after driving in snow and icy conditions. Took it to the shop - they say its the rear left abs sensor according to the codes. Sensor had to be ordered so I took it home - without the abs relay in as the system had been coming on and off. Noticed that the odometer was running fast - even when with the car at standstill - putting the abs relay back in does not change anything. Speedometer seems to work normally. Questions: Does the odometer use reading from the rear left abs speed sensor? If not, is there something than can cause both problems? Bad grounding? Some control unit?