Revealing mistake: In the scene where Cooper takes the homeless man's photo on his iPhone, if you look to the bottom left of his iPhone's screen where it shows pictures that you have already taken, you can see that the homeless man's photo has already been taken, indicating that perhaps this scene was shot a few times, and the photos taken during those scenes were never deleted.
Episode #1.4 - S1-E4
Revealing mistake: Mrs. Weston's baby is obviously a doll.
Withdrawal - S2-E1
Revealing mistake: At 46:24, Peter and Mozzie are sat on a bench. Peter's paper has the exact same wording on back pages as well as the front page. (00:46:24)
Revealing mistake: When Soliday becomes possessed and grabs the steering wheel of the car, you can see the small explosion effect that causes the car to flip.
The Royal We - S3-E2
Revealing mistake: On the RV of the guy being accused of molesting the girls, someone has written "PERVERT" in red spray paint. At a point you see Lightman next to a car, and the RV in the background, and the text is mirrored reading: "TREVREP", showing that during editing, this shot was flipped. (00:15:30)