RICHARD: Perhaps instead of that horrible salmon that keeps showing up.
EMILY: That salmon is a fine delicacy.
RICHARD: Mm, potato, po-tah-to.
Richard is referring to the song Let’s Call the Whole Thing Off, written by George and Ira Gershwin, where the lyrics say, “You like potato and I like po-tah-to, You like to-may-to and I like to-mah-to”. The characters decide that their differences, such as the way they pronounce certain words, are not worth ending their relationship over.
The song was written for the 1937 musical comedy film Shall We Dance?, directed by Mark Sandrich and starring Fred Astaire and Ginger Rogers. The film wasn’t a raging success, but the song has proved enduring, being often re-recorded and used in other films.
When people say “potato, po-tah-to” (or “to-may-toe, to-mah-to”), they mean that the difference of opinion they are having with someone is trivial and not worth arguing about.