When Magnum was forced out of the car, his phone was in the hands-free cradle on the dashboard. After the car pulled away, he took the phone out of his pocket.
The first high-speed chase covers the same block of King Street multiple times in a few seconds. Note the Walmart is still nearby long after the cars should have sped past.
When Magnum turns around after receiving the phone call on the beach, the tracks from the camera car can be seen.
When Magnum and Rick are chasing the Chrysler and the police are chasing both, they are actually headed the wrong way on a one-way street. This can be seen as they are using all lanes in their direction while cars are parked on both sides in the opposite direction and the traffic lights are facing the wrong way.