Deliberate mistake: When the investigators are in the basement wine cellar, they turn on their flashlights to illuminate the pitch black area as they walk around. However there is a light source moving with the camera shining on them as they are casting a shadow behind them.
Continuity mistake: Lisbon and Jane enter the interrogation room to interview the wife of the murder victim. As Lisbon sits down she opens her notepad upside down. Next shot of her the notepad is right side up. Remaining shots of Lisbon shows the notepad upside down again.
Continuity mistake: S02E06 - Black Gold and Red Blood. Lisbon comes to visit Jane in prison. She brings him a muffin in a white paper bag. In shots facing Jane, the bag faces outward. In shots facing Lisbon, the bag faces towards the middle of the table.
Other mistake: When Jane is setting up for his escape from prison, he captures a wild mouse. Then he presumably holds her in his hand for the whole time. I've handled mice, and when they're scared, they bite hard enough to take chunks out. There's no way a wild mouse would stay in human's fist that long without drawing blood.