Red Dawn's US release date was August 10, 1984
The Flamingo Kid's US release date was December 21, 1984
Indiana Jones' US release date was May 23, 1984
However, IMDb's site lists the rating for IJ/Temple to be PG (Click here and scroll down to "Also Known As" and on the last line you'll see the rating "USA: PG")
For the longest time, I was under the impression that Dreamscape was the first PG-13 film (August 15, 1984), but Red Dawn beat it by 5 days apparently.
Here's real trivia for you, John Wayne's "Big Jake" (1971) is rated PG-13 as well. So is Alfred Hitchcock's "The Birds" (1963).