While Danny and Tani are riding in the car, Tani's shoulder belt alternates between flat and twisted on her shoulder.
When Steven and Duke goes to California to take down Scott Hester, they are on their own. But they have no jurisdiction in California, and would have had to be accompanied by either local or state law-enforcement, which also technically would make the arrest.
Steve's dad was shot on May 14, 1983, per the police report. Steve is seen watching "Inspector Gadget" on that day, but that animated series did not premiere until September 12, 1983.
The Makua Keaau Forest scene took place in 1983, and the police cruiser used in that scene is a smoother-nosed 1988-1989 Mercury Grand Marquis. The law enforcement departments in the United States and Canada used Ford LTD Crown Victoria S, which came specifically with factory-equipped police package, instead of plushier and more expensive Mercury Grand Marquis.