Revealing mistake: When McCluskey is lying on the floor inside the restaurant after getting shot dead, he blinks.
Suggested correction: I just watched the scene; he doesn't blink. The shot is very wide, and his eyes are barely visible in the frame anyway, but even paying very close attention to McCluskey, there's no blinking.

Continuity mistake: When Sonny is shot at the toll booth the front windshield is torn apart by bullets yet when the bodyguards arrive thirty seconds later, the windshield is intact. (01:53:20)
Suggested correction: Look again, the broken windows you are seeing are from the side windows, the windscreen was shot out entirely.
The screenshot shows the windscreen is intact after being shot out.
Factual error: Fredo is wearing a very 1970's sport coat, sunglasses, and wing-tipped shirt ensemble in the Las Vegas hotel scene, set some 20 years earlier.
Suggested correction: This kind of style existed at the time the scene was set; even then, Vegas had its own eccentric style. You can see plenty of photos of people from that time dressed like Fredo is.
Factual error: At the end of the movie, when Michael's car pulls up in front of the Las Vegas hotel, if you look through the glass windows, two men wearing 1970's shirts and gold neck chains, with "hippie-style" haircuts walking through the lobby, though this is supposed to be in the late 40's or early 50's. (02:13:50)
Suggested correction: Similar to another entry about the supposed anachronistic style of the Vegas scenes, the style was not unheard-of at the time, especially in Las Vegas, where people tended to dress a little more outlandishly.
Factual error: When Luca Brasi goes to meet the Tattaglia family and Sollozzo to pretend he would like to defect, and they garrote him, Brasi is making all kinds of loud noises while being strangled until he dies. During choking or strangulation, one is unable to make much (if any) sound because air cannot pass through the vocal chords on its way out of the body just as it cannot enter the body and get to the lungs. (00:41:25)
Suggested correction: By tightening the neck muscles, one can resist strangulation, especially if one is stronger than the person strangling you. Luca is very physically powerful and so resists in this way, which is why he is able to make gargling noises as he struggles. Eventually, though, the reduced oxygen takes its toll, and he succumbs.
Continuity mistake: Before Luca Brasi's hand gets pinned to the counter by Sollozzo's knife, Tattaglia holds it down on the counter with both hands, but then, in a close-up of the stabbing, Brasi's hand is hovering over the counter and Tattaglia's hands are nowhere. (00:41:20)
Suggested correction: Incorrect. Throughout the murder, Tattaglia holds Brasi's left-hand down, with both his own, while Solozzo stabs Brasi's right hand with the knife, which pins it to the table. Any apparent "hovering" is due to Brasi struggling to lift his knifed hand. There is no point where this changes.
Revealing mistake: When being transferred to another room the supposedly unconscious Don pulls his left arm up so it won't hit the door frame.
Suggested correction: He's shown to be awake when Michael is talking too him moments later, albeit weak. He was probably woken up by the movement before this point, so he was conscious enough to move his hand.