The Man with the Umbrella - S1-E3
Plot hole: With all the cameras and guards watching, there's no way anyone would be able to use a cigarette lighter to help them pass the game.
Other mistake: SPOILER! The fourth game (the game with the marbles) can only be won when you win your opponents' 10 marbles and hand over a bag with 20 marbles (as is shown at various points during the game). But at the beginning of E7, Seong Gi-Hun (the main character who defeated the old man) takes a marble out of his pocket. This means he handed over only 19 marbles and should have been eliminated.
The Man with the Umbrella - S1-E3
Continuity mistake: Toward the end of episode 3 when player 119 stabs a guard in the eye and takes his gun, he then shoots a second guard in the left arm and holds him hostage. However, after Player 119 sees his guard-hostage is a very young man and decides to kill himself, we see the Front Man walk up to the scene and in that moment the guard-no-longer-hostage has obviously been shot in the right arm. Noticing this made me realise the jungle gyms on either side of the scene got swapped. It's a mirrored image. (00:47:07 - 00:49:03)
Red Light, Green Light - S1-E1
Revealing mistake: In LGL, if you look at the map of players, look at the player top right of 456 which is player 415. It is a balding man with glasses. Yet during the massacre of LGL, you see at the doors that player 415 is a woman with long hair in a pony tail.
The Man with the Umbrella - S1-E3
Continuity mistake: The umbrella shape on the wall changes in between scenes from wavy lines at the bottom to straight.
Visible crew/equipment: When the old man is remembering his childhood home and walking around as the game is winding down, he walks toward the camera. This is a handheld shot. The shadow of the camera is on his shirt briefly.
The Man with the Umbrella - S1-E3
Visible crew/equipment: When the second game starts and everyone is climbing up the stairs, two of the players are talking. The camera is in front of them going up the stairs. At one point you can see the shadow of the camera on the wall to the left.