Yankovic worked with experienced Times puzzle constructor Eric Berlin, who's created 40 puzzles, to serve up the clues. An accompanying Times story (spoiler: it includes the answers) explains that the theme takes movie titles and gives them cheesy twists, so the Tom Cruise 1992 legal drama "A Few Good Men" becomes "A Few Gouda Men."
There are other clues that seem to be right up Al's pop-culture alley, including "supply for Wile E. Coyote" (sorry, ACME is one letter too long) and "___ dead, Jim" (Star Trek fans, boldly go try it). One is a nod to another humorous songwriter, the legendary Tom Lehrer. ("Satirist Tom" is the clue, but c'mon, that was a gimme.)
If you have online access to the Times, you can work the puzzle here. Don't like puzzles or parody? Then frankly, my dear, you probably don't give edam.