After leaving Rita's place the first time, Rockford's getting into his car, the sound of his door closing wasn't included on the soundtrack.
In the scene where Jim and Rita are staking out The Canadian American Trading Company, when Mr. Woodruff comes out of the building and gets into his limo, Jim reaches for something, seemingly to start his car to follow Woodruff, and the sound of an engine starting is clearly heard, the keys/ignition are clearly visible, but Jim does not touch the keys before or while the engine is heard to start.