I just saw James Doohan in the 1965 movie The Satan Bug. It was an uncredited, non-speaking part, but he had a fair amount of screen time as, essentially, a redshirt (or rather, the junior member of a pair of ill-fated federal agents). The movie also featured TNG guest star John Anderson, and was scored by Jerry Goldsmith.
He is also in The Wheeler Dealers
, a 1963 comedy with Lee Remick and James Garner. He is in it at the very end, in the climatic trial scene playing Garner's attorney. He has a few lines, but is uncredited (credits in movies started getting more complete with movies like The Godfather
). That scene alone is chock full of familiar TV faces like: John Astin, a pre- Laugh-In Alan Sues - who gets to roll his eyes, Jim Backus, Jack Benny's old bandleader, Phil Harris, and so on. The judge is a guy named Charles Lane, who was THE guy playing business execs, judges and bankers in sitcoms. He was almost in more Bewitched episodes, than some of the cast members. Surprised HE never showed up in Trek -perhaps Nilz Baris. Its on TCM quite a bit, so its worth catching.