Chapter One: The River's Edge - S1-E1
Revealing mistake: When Hermione opens the bag of money, one stack says "Motion Picture Use Only." (00:29:45)
On the Road - S2-E1
Revealing mistake: As Cassidy, Tulip, and Jesse are trying to outrun a police car, another cop car enters the road in front of theirs with tires squealing. There are tire skid marks On the Road before the cop car enters, indicating previous takes of the same stunt.
Revealing mistake: When Bob and Joyce have lunch, Bob pops open a can of soda (which is period appropriate). The scene cuts to Joyce, then back to Bob. It is clear from how he is holding the can, and how he pretends to drink from it, that his newly opened soda is actually empty.
Revealing mistake: A typewriter is being used, but the carriage is not moving. (00:42:50)
Revealing mistake: When the president talks to the reverend in the Oval Office, the picture of President Lincoln is either higher and then lower when it is shown.
Revealing mistake: Right after the scene in Wallace's office where the DHS tries to shut down Hayes' investigation, the scene shifts to a montage. Towards the end of it there's a loop: in the bottom left corner you can see someone on a scooter appear from the left, only to disappear a second later and reappear from where they'd come the first time. (00:20:00)
Revealing mistake: When the sniper is aiming at Swagger and the soldier through the window, a woman walks in and notices him. He shoots her and she falls. The problem is, he shoots at nothing. She simply turns her head and acts like she got hit. There's no indication a bullet even hit her.
Fence + Suitcase + Americium-241 - S3-E12
Revealing mistake: When MacGyver cuts the green wire under the bomb, the wire is not tied up at both ends. (00:25:45)
Revealing mistake: As Sgt. Cain and Chief Lain stand by Marjorie's dead body lying on the hotel bed, discussing her death from an overdose, you can see her stomach rise and fall slightly, though she's supposed to be dead. (00:18:00 - 00:20:00)
Revealing mistake: Janet is holding a coke in her hand that she is supposed to be conjuring up but is already holding it.