Audio problem: During the scene where Sean goes to the doctor and they are trying to diagnose his shaking hand ('yip') condition. When the doctor and Sean stand up at the end of the consult, the doctor continues speaking to Sean, but his lips do not move.
Mrs. Grubman - S2-E4
Revealing mistake: Mrs. Grubman is lying in the coffin. She noticeably swallows when she is supposed to be dead.
Agatha Ripp - S2-E8
Audio problem: When Christian is returning to the office and sees a crowd of people outside hoping to see Agatha (who they believe has the stigmata of Jesus Christ), he runs into a couple with their infant. Christian asks if their baby is sick, and the couple shows him the backside of the infant where it has a vertebrae "tail", and they then ask him if they can see Agatha. During this sequence, we can hear loud crying, but various camera shots show the baby's face and she/she is not crying.
Other mistake: When Sean is on the phone with Julia, by mistake he accidentally calls Julia "Julian." Julian is the first name of the actor who plays Christian.
Factual error: At the onset of the episode, Christian and his blind girlfriend decide to go to a movie rental place. While Christian goes inside, he leaves his gf in the car and the song "Love Will Keep Us Together" by Captain and Tenille is playing. During this time, two young guys pull up in a van and find out the girl is blind and then decide to strip Christian's car of all 4 wheels and the front end. Christian comes out about three minutes later (the end of the same song is nearing) to see his car sitting on 4 jacks and void of any wheels or front end. Given the time that Christian is gone which is just a few minutes, it is nearly impossible for even a team of multiple seasoned pro thieves with the most sophisticated auto equipment to disassemble part of a car (and those specific parts) in that small amount of time, let alone two kids just passing by deciding to do so on the spur of the moment.
Chosen answer: "So Damn Beautiful" by Polaroid.