The first Coyote was built from a Manta Montage kit car. The second, used later in the series, was built from a DeLorean DMC-12. Reportedly the car was changed because the two men ( who both stood six feet tall ) had a hard time getting in and out of, as well as sitting in, the kit car.
Originally the concept was to have Hardcastle to hunt down all the criminals he prosecuted but were released due to technicalities. In order to keep the A.C.L.U. off of their backs, the producers decided to have him go after them for current offenses only.
Judge Hardcastle's nickname was "Hardcase".
In the pilot episode you can see the gear shifter of the Coyote directly on the floor. By the later episodes you can see a gated shifter and center console and when they show tachometer it has a Ferrari logo. Possibly stock footage from Magnum, P.I.
Gary Hymes can be sometimes be seen driving the Coyote, including in the very beginning of the first season opening credits. He looks a little like Larry Fine.