I have had a great stroll down TV memory lane with this thread. Some web surfing found some great sites. This one here references the 16570:
http://magnum-mania.com/Characters/Main_Characters.html
And while the show started in '79 (pilot?), I think, he didn't start wearing the Rolex until season 4 or so, which gives further credibility to the ACTUAL watch being a 16570.