Under the Cloak of War - S2-E8
Other mistake: The Klingon ambassador burns his hand when grasping a goblet. It is the palm of this hand that is burnt. When he is treated in Sick Bay with a dermal regenerator, it is being used on top of his hand.
Star Trek: Strange New Worlds (2022)
1 other mistake in Under the Cloak of War
Starring: Rebecca Romijn, Anson Mount, Gia Sandhu
Character mistake: The Enterprise is targeted by projectiles from the planet. Spock identifies them as "plasma torpedoes", and Captain Pike reacts with surprise; "Plasma torpedoes? That's 21st century tech" and from that they all establish that the civilization they contacted is not yet capable of warp drive. Plasma torpedoes are the main weaponry of the Romulans centuries later, and Earth itself did acquire warp drive in the 21st century, so this claim and deduction don't seem to add up. (00:22:15)
Trivia: For anyone curious, the quote "I pretended to be somebody I wanted to be until finally I became that person. Or he became me" was said by Cary Grant - to Pelia, clearly.