Is There in Truth No Beauty? - S3-E5
Other mistake: In the final scene, Kirk is still in the transporter room, but does not have on a visor when the ambassador transports out. Even if he did, humans can still go mad if wearing one and that's why Spock operates the transporter. Spock has his visor on, but then you see Kirk walk out of the transporter room without a visor and he is not going mad.
Other mistake: The episode's action takes place around 11:00pm (night time), yet all the scenes show broad daylight.
Other mistake: After King Tut's men deliver the statue, it's referred to as a Sphinx. Even Batman says, "Rather good imitation of the 4th Dynasty's Sphinx at Giza." Problem is, the Great Sphinx of Giza is a reclining lion with a human head. The statue in Gotham's park is a ram's head atop a seated human body, resembling Egyptian God Khnum, and looks nothing like the Egyptian Sphinx. Bruce Wayne is a member of Gotham City Museum's Board of Trustees, which recently opened the new exhibit of Egyptian antiquities. (00:10:35)