A code P0500 means that one or more of the following has happened:
· The Vehicle Speed Sensor (VSS) is not reading (functioning) properly
· There is a broken/frayed wire leading to the vehicle speed sensor
Take it back to the tranny shop and have the correct this. Good luck!
I suspect your mechanic did not reconnect your speed sensor (VSS) correctly or damaged the electrical connection when they did the tranny work. Newer cars like yours no longer have a speedometer cable but rather use an electronic sensor attached to the transmission or the rear differential. The VSS not only controls the speedometer but also some other functions like the transmission shift points, the cruise control and ABS brake system. The P0720 code is for the "Output speed sensor" which is also attached to the transmission and probably was not reinstalled properly. The P0731 is just an incorrect gear code being thrown because of the other two problems.