Formal:
* Faux pas: A social blunder or mistake.
* Mishap: An unfortunate accident or error.
* Gaffe: A careless mistake, especially in a public situation.
* Slip-up: A minor error.
* Blooper: A humorous mistake, often made on stage or in a film.
Informal:
* Fumble: A clumsy or awkward mistake.
* Oops: A casual exclamation expressing regret for a mistake.
* Whoopsie: A lighthearted expression for a small mistake.
* Boner: A slang term for a serious mistake.
* Epic fail: A significant and embarrassing failure.
* Face-palm: A gesture of embarrassment or frustration.
Specific:
* Foot-in-mouth moment: Saying something embarrassing or inappropriate.
* Brain fart: A temporary lapse in memory or concentration.
* Dumb mistake: A mistake made due to carelessness or lack of thought.
The best word to use will depend on the situation and your desired tone.