Continuity mistake: As Lionel says "Good morning, Miss Sullivan." there is a camera change from Chloe's left to her right. When the camera is on the left, her left arm is down. When the camera jumps to her right her left arm is now in the middle of placing something high up on the layout board she is using.
Continuity mistake: Just before Lex has his father arrested they are talking while Lionel sits behind his desk. In the shot of Lionel from his side of the desk there is a flat panel monitor behind his keyboard. In shots from Lex's side of the desk the monitor is gone. It returns as FBI agent Loder walks in and Lex stands up.
Continuity mistake: After Lionel finds out about the wire that Lex has been wearing, he sits down and tells Lex to get out. As Lex leaves, in the wide shot, Lionel drops his hands down to his lap. In the zoomed in shot Lionel's hands are up to his face as he plays with the wire. There was no time for him to make that move between shots.