Not in the Line of Fire - S3-E15
Revealing mistake: Two thirds of the way into the show, Mike and the mayor are talking in his office. If you look at the Mets hat behind Mike, the NY emblem is upside down.
Taxi Driver - S3-E13
Visible crew/equipment: Just after Mike sees everyone as Nicki and tells them to leave, a boom mic can be seen at the top of the screen. (00:00:50)
Visible crew/equipment: When Stuart and Carter wake up in the same bed, the shot pans to the right and a boom mic is seen at the top-right corner of the screen, frantically trying to get out of the camera's view.
Not in the Line of Fire - S3-E15
Revealing mistake: When James points out to Carter that Rags is eating his sleeping pills, it's painfully obvious that they are actually dog biscuits. (00:06:15)
How to Bury a Millionaire - S4-E8
Factual error: It is implied, and later showed, that Who Wants To Be A Millionaire is broadcast live, which in fact it is not. Furthermore, the winner of $1M only gets $100K within the first month of their appearance and the remaining amount much later, based on the broadcast schedule. Nikki could not have watched Paul winning his money in real time, let alone in the evening.
O Mother, Where Art Thou? - S6-E13
Factual error: It is stated that the Mayor is 56 and his mother was, upon her death, an organ (heart) donor. Assuming she was at least 15 when she had him, she was at least 70 when she died. Seventy is out of acceptable boundaries for organ donors, especially if the recipients were to be close to a decade younger. Recipients on waiting lists nearly always receive their organs from sudden death victims with the organ (heart) in a perfect condition. A 70-something woman's heart can not outweigh the risks of the procedure.
Visible crew/equipment: Just after Trevor gets off the bus, a boom mic dips down into the shot at the top of the screen. (00:08:05)
Visible crew/equipment: Just as Caitlin enters Mike's office when Trevor is looking for her, a boom mic can be see at the top of the screen. (00:04:45)
Visible crew/equipment: When the Mayor gets up to leave the therapist's office with Mike, a boom mic can be seen in the top-left corner of the screen. (00:14:10)
Revealing mistake: When the doors to the barn magically fly open to reveal that James has returned, you can see it being opened by someone through a crack in the wall.
Revealing mistake: Whenever the judge's hands are shown, his extra fingers are always unquestionably rigid and still, even while writing. This shows that they are prosthetic (although meant to have been there by birth, which he explains).
Visible crew/equipment: When Mike, Caitlin, and James are at the barn, a boom mic can be seen at the top of the screen. (00:11:00)
The Marry Caitlin Moore Show - S4-E15
Visible crew/equipment: When Caitlin is talking about her plan to get back at the opponent for Senate, a boom mic can be seen at the top of the screen. (00:03:20)
A Tale of Two Sisters - S4-E13
Visible crew/equipment: When Stuart gets onto the platform to disrobe, a boom mic can be seen directly above his head. (00:16:05)
A Tale of Two Sisters - S4-E13
Visible crew/equipment: Just after Mike and Catherine get back to the former's apartment, a boom mic can be seen at the top of the screen. (00:12:25)
My Dinner with Caitlin (a.k.a. Christmas 1999) - S4-E12
Visible crew/equipment: When Nicki goes to talk to the depressed man on the couch, a camera moves into the frame, seen in the upper right corner of the screen. (00:17:45)
My Dinner with Caitlin (a.k.a. Christmas 1999) - S4-E12
Visible crew/equipment: When the homeless man states that he wants Paul's headband, a boom mic can be seen at the top-left corner of the screen. (00:08:15)
Visible crew/equipment: When Mike and Caitlin are at the pound to get the Mayor's car, a boom can be seen at the top of the screen just as Mike is about to talk to the attendant. (00:10:35)
Visible crew/equipment: Just after Nicki talks to Carter about wanting her picture retaken, Stuart enters the bullpen and two boom mics are visible at the of the screen. (00:05:10)
How to Bury a Millionaire - S4-E8
Visible crew/equipment: Just after Mike opens the door to his office to tell Stuart that they are planning to keep the Mayor in the well for a bit longer, a camera moves into view on the left edge of the screen. (00:11:50)