Dr. Strangelove?
What about Hitchcock? Psycho, The Birds, North by Northwest is 1959 which is close enough.
Anatomy of a Murder is also 1959 I think but is a great trial film.
Don't know how much these fit into what you want.
There's the spaghetti westerns like The Good, The Bad and The Ugly.
A Shot In The Dark is my favorite of the Pink Panther series by far and one of my favorite comedies, the original is good too. Both early 60s.
Speaking of Sellers and James Bond, there's Casino Royale. :lol
Continuing with Sellers, The Party is late 60s and basically him improvising for an hour and a half.
And Manos, of course.
awesome