Continuity mistake: When Mc Murphy is strangling the nurse at the end, from above his hat is lying on the floor, but when you see the shot from her angle, he is wearing it again. (01:56:55)
Continuity mistake: You see an opening scene where McMurphy is arriving by automobile. When he gets out of the car it is a cloudy dark day. A few seconds later when he is being brought into the hospital with the guards we see them entering the front door together from down the hallway. Now you can see that it is a bright sunny day outside. (00:04:20)
Continuity mistake: When the inmates return from their fishing trip and the boat enters the haven the sky is overcast, but a moment later we see the sun shining on the people waiting for them at the quay. (01:02:55)
Continuity mistake: In the scene where McMurphy gets upset while playing blackjack, he gets up and walks towards the nurses' quarters to turn down the volume on the record player. Martini and Bibbit are still sitting at the card table while McMurphy is walking towards the nurses' quarters but when he gets inside, Martini is already leaning against the counter of the nurses' quarters with Bibbit close behind him. (00:27:00)
Continuity mistake: There's a problem with McMurphy's collar when he is delivered to the clinic: Till the moment he kisses the policeman good-bye his right collar is under and the left collar is over the jacket, thereafter it's the other way round. (00:05:20)
Continuity mistake: In the scene where the patients are arguing over cigarettes and tossing one around from patient to patient, the cigarette varies in length from long to short and back again as you see different shots of patients getting the cigarette. (01:12:40)
Continuity mistake: When Billy is found after his suicide Harding, Martini, Sefelt, and Scanlon come rushing to the room one after the other. Seen from inside Sefelt and Scanlon have switched places. (01:55:55)
Visible crew/equipment: In the second basketball scene, when McMurphy shouts at Martini because he threw the ball against the fence, there's a lot of equipment visible on the left side, most prominently a big spotlight. (01:05:20)
Continuity mistake: In the scene where the boys are playing blackjack, watch McMurphy's cigarette as he talks to Martini about the rules of the game. It changes length throughout the scene. (00:26:10)
Other mistake: In the scene where the Chief smothers McMurphy, when the Chief pulls the pillow away from McMurphy's face, you can see McMurphy's tongue moving up and down even though he is supposed to be dead. (02:03:45)
Continuity mistake: When McMurphy is brought to the ward after his brain surgery one of the males nurses puts a bag on the end of his bed. When they walk away the bag has disappeared. (02:00:20)
Continuity mistake: When the guys go fishing on the boat and one of them catches a fish, they panic, and the boat starts to go in circles. In the close up shots and the wide shots in that scene the sea is very different from shot to shot. (01:02:10)
Continuity mistake: When McMurphy is doing the TV commentator he starts quite a riot. We see Sefelt banging with a brush on a dustpan, but between shots the brush disappears and the dustpan is in the other hand. (00:47:00)
Continuity mistake: When McMurphy climbs over the fence onto the tree and falls on the ground his shirt is more or less in order. When he gets up it's hanging over his right hip. (00:51:05)
Continuity mistake: In the "therapy" session where McMurphy discovers that most of the inmates are here voluntarily he first looks as if he hasn't shaved for days, but in the second half of the scene he is clean-shaven. In the same session the writing on the board behind Nurse Ratchett changes: It says "No smoking in pool area", but when she says "You're making some very challenging statements" the text disappears for one shot. (01:09:35 - 01:10:35)
Visible crew/equipment: When McMurphy tries to make the "dancer" vote for the world series he dances with him through the hall. When he does that you see the shadows of the boom mike and cables on them. (00:43:50)
Continuity mistake: When the chief gets his first basketball lesson his ear does or does not stick out through his hair in alternating shots. (00:21:55)
Revealing mistake: If you look closely at the scene where McMurphy climbs the fence and falls from the tree, Nicholson's stuntman looks nothing like him.
Other mistake: The movie is a time piece set in the year 1963. After McMurphy jumps the fence, there is an orange/red Ford Pinto in the scene. Ford Pinto's weren't introduced until 1970. (00:51:27)
Answer: It's better explained in the novel, where the Chief is the narrator. Essentially, he played deaf and dumb, so he'd be left alone by the Nurse and the staff; seeing what they did to the other patients, he figured the less he was noticed, the better. In this way, he is privy to a lot of the seedier goings-on, since they don't think he can hear what they're saying or tell anyone what he's seen.