Continuity mistake: For the first episodes (minus the plot), the opening of the series features the Ferrari with two different license plates. The opening shot shows the ROBIN-1 vanity plate that is in every episode but not in the most well known version of the opening (with the iconic Mike Post theme music used in all the other seasons), and the following shows the license plate from the pilot.
Revealing mistake: In the opening of the second third of the season (the one with the iconic Mike Post theme) there is a brief scene with a car propelled in the air by an explosion. It's an outtake from the pilot movie, since the banged up car is very recognizable, but it's also easy to see why it was an outtake; you can easily see cables used to make the car fly in the air. Also, that car was not in an explosion in that episode.
Other mistake: With episode 11, "Thicker Than Blood", the opening changes to the truly iconic version associated with the series, with a large overhaul of footage. There must have been some hiccup making it though, because the title of the series appears as "Magnum PI", no punctuation. There's a version of the opening that includes the correct "P.I." title card.