Triumvirate of Terror! - S3-E8
Continuity mistake: To protect Bruce Wayne's identity from Lex, Alfred dons the Bat Suit and fights Lex to give Bruce enough time to get another bat suit on. Lex uses a laser to cut through a catwalk that Alfred is walking on and he falls. He is in front of Lex but at a distance. The real Batman walks up to Alfred and thanks him, then charges Lex. Suddenly he is behind Lex when doing this and Lex has to turn around to defend himself, despite just being focused where Alfred was. (00:15:20)

Triumvirate of Terror! - S3-E8
Continuity mistake: After teleporting the villains and heroes to Lex's lair, Lex has his hands gripping a control panel podium in front of him. As Joker begins to speak, it cuts to a closer angle and suddenly Lex's arms change position and his hands are gripping the podium differently. (00:17:05)
Triumvirate of Terror! - S3-E8
Continuity mistake: Lex teleports Superman, Batman, and Wonder Woman to his lair and begins broadcasting to the world. Cheetah raises both arms in a wide shot and brags about how the world will see now, and lowers her left arm while keeping her right one up. Then it cuts to a closer view and both arms are up again, and she again lowers her left arm. (00:17:45)

Triumvirate of Terror! - S3-E8
Continuity mistake: As the camera comes out so Lex can broadcast the death of the heroes to the world and beyond, they are standing with Cheetah on Lex's right, and Joker to his left. But then when the shot shows a large screen where the broadcast is happening, Cheetah walks in on his left and Joker is now on his right. (00:18:00)
Chosen answer: The Star Sapphires are agents of the Zamarons, the female species of the Guardians of the Universe, they are enemies of the Green Lanterns, which is why Carol has anger toward Hal. It should also be mentioned that the further a ring is from the center of the "The Emotional Spectrum", the more control the ring has over the user.
MasterOfAll