Strawberries and Cream: Part 1 - S3-E23
Plot hole: In the heat of killing fake Red John, Jane forgot to notice that Craig O'Laughlin never knew about the mall setup to lure Red John. So definitely Gale Bertram himself was in contact with the serial killer which he may have missed first up, but all that time in jail afterwards he could have figured it out.
Strawberries and Cream: Part 2 - S3-E24
Continuity mistake: In S03E10 Patrick Jane obtains Laroche's suspect list "through back channels" from Virgil Minelli. In this episode Patrick Jane obtains Laroche's suspect list again, through bluffing with what Laroche is hiding in his safe.
Every Rose Has Its Thorn - S3-E19
Continuity mistake: In the scene where Agent Lisbon is asking Jane why he's obsessed with the woman he's investigating, Lisbon's pen is in her right hand. But when she waves, the pen has disappeared, but in the next shot it's back in her hand.
Continuity mistake: The murderer is running full speed directly at Grace, who moves to intercept him. In the next scene she is shown bringing him down from behind.
Every Rose Has Its Thorn - S3-E19
Continuity mistake: In the beginning when Patrick is talking to the widow Erica Flynn at the police station, when she first leaves the interrogation room the zipper in the back of her dress is down about four inches. As she is walking to the elevator, when she goes into the elevator and turns, you see that it is now zipped up completely.