In many episodes, cars and uniform patches saying "state police" are shown. Hawaii is the only US State without a state police agency, but instead its law enforcement is performed by county governments.
TC is always shown flying his Hughes 500 helicopter from the left seat. The pilots seat in the Hughes 500 is on the right side.
In many episodes, it shows a view through a sniper's scope, but without a central point of reference in the scope. All rifle scopes have some means of telling where the center is, such as crosshairs.
In the opening credits when Magnum and Rick are in the Ferrari you can see the camera and dolly reflection in the rear window.
Throughout the series there are scenes when a kookaburra can be heard. Kookaburras only live in Australia.
Hawaii has some of the most stringent firearm laws in the United States. It is nearly impossible to obtain an open or concealed carry handgun permit, and as of 2017, less than 200 people on all of the islands of the state, not including law enforcement officers, have an open or concealed carry handgun permit. Yet the entire series shows all of the major characters both armed with handguns and freely carrying and using them. This would not be possible.
Despite being only a private detective, Magnum is involved in the deaths of at 15 people during the run of the series. Yet he never faces any criminal prosecution for this, even though at least three of these events were clearly cases of premeditated murder.