Kirk and Khan never meet face to face
The film features some of the best dialogue between James Kirk and Khan Noonien Singh that one could hope to write. Their on-screen chemistry crackles and sizzles as the two men harass one another. Due to the creativity in the dialogue and the constant times people have quoted these scenes, you'd be forgiven if you never knew that the two men are never actually on screen with one another.
Neither William Shatner (Kirk) Or Ricardo Montalban (Khan) ever actually appeared with one another on screen. Instead, all of the scenes where the two characters are talking to one another were filmed separately and edited together. It was certainly a bold choice and one that wasn't always meant to be.
There was originally an idea of having Kirk and Khan fight in person, but as film director Nicholas Meyer once told TrekMovie, the last time they did that idea it looked "corny" to him so he didn't want to redo it on the big screen even if it was meant to be more of a shootout idea.
The decision to hold off worked wonders for the film. Instead of a forced fight that would've been limited due to the lack of advancements in the 1980s, Wrath of Khan was able to show the two men on even terms, as captains and leaders, which allowed Kirk to earn himself a win in a more believable manner.