The check engine light is most likely due to the P0137. That code is for the post cat O2 sensor. Not a huge concern as it will not affect engine performance at all. The P0501 is for the speed control sensor. A quick search on the net came up with this. Hope it helps:
Vehicle Application: 2004 Jeep Liberty Sport 3.7L
Customer Concern: No speedometer or odometer operation. Sets code P0501.
Tests/Procedures: 1. Using a compatible scan tool, check the vehicle speed signal in the Body Control Module (BCM) and Powertrain Control Module (PCM). If differences are seen, check the Light Green/Yellow signal wire between the controllers, the PCM puts out a 5v to the BCM and it pulses it to ground.
2. Check the signal wires to the BCM, the Pink/Orange is the supply to the sensor and the Dark Green/Orange is the signal wire.
Potential Causes: Body Control Module (BCM)
Instrument Cluster (IC)
Powertrain Control Module (PCM)
Rear Wheel Speed Sensor
Wiring Harness
Tech Tips: If the vehicle is not equipped with ABS brakes, the speed sensor is wired directly to the BCM. Test for battery voltage on the Yellow wire to the speed sensor. This voltage comes from the BCM. The other wire is the signal wire and should have a square wave signal, with the vehicle moving.
Diagnostic Codes: P0501