When Michael moves his father's bed from the hospital room into the hallway, there is a sign on the wall over Michael's shoulder which lists Robert O'Lowery as the Fire Commissioner. He was Commissioner in the 1970s, not the 1940s (it should have been Patrick Walsh).
Michael reads a New York Mirror newspaper account of his father's brush with death. The page is fabricated but inserted into an actual newspaper, which appears to be the NY Daily News. The Daily News page on the opposite side shows a story about a Catholic mass celebrated at St. Patrick's Cathedral, written by a reporter with a Hispanic surname. A minority's byline would never have appeared in the News at that time; minorities did not attain the status of reporters at that newspaper until the late 1960s or early 1970s. Also, the barely readable text in the story says the mass was said by Terence Cardinal Cooke, who was then a parish priest and did not become a cardinal until 1969.
When Michael is arriving in Las Vegas, supposedly set in the very early 1950s, when he, Fredo, Tom and others are getting out of the car in the hotel driveway, two long-haired, bearded "hippie types" from the early '70s can be seen through the window in the lobby. (In the DVD commentary, Francis Ford Coppola admits that he is embarrassed by this oversight, but that the shot was done on the cheap by the second unit.)
Tom Hagen flies to California to see the movie producer in a Lockheed Constellation. The first production model of the Lockheed Constellation was not produced until 1947, and did not enter commercial service until even later. Tom's flight was apparently in 1945 ("almost 1946" according to movie dialog).
The accordion played in the wedding scene was an "Excelsior" model that was not manufactured until the 1950s. The same goes for the "prop" accordion seen in the shoot-out, where the accordion is on a chair with the bellows open. The older accordions did not have the same features.
When the funeral procession drives into the graveyard, 1970s 18-wheelers and vehicles can be seen on the freeway at the top left and top right of the scene. The freeway with these vehicles is visible throughout the scene during various shots.
There is a newspaper shown with the article about Don Corleone's discharge from the hospital. In the lower right is a Table Of Contents, with the first item "TV-Radio Listings." If TV listings existed at all in 1946, they would not be noted before radio listings.
When Michael finds his father without protection in the hospital, he picks up the phone by the bed to alert the family. The receiver has a curly cord which wasn't available until the mid- to late-1950s.
As Vito Corleone comes home from the hospital, a newspaper article is shown that reads "Syndicate Big Shot Corleone Goes Home" the table of contents shows "TV / Radio" listings. It's unlikely TV listings were in the newspaper in the 1940s.
In Vito's brush with death, one hitman's pistol emits a muzzle flash, visible just after a cut to the overhead shot of them running away, but there is no accompanying sound effect for this last gunshot.
When Tom Hagen is trying to convince Sonny not to go to war after Vito Corleone was almost murdered, he states that the Corleone family will be outcasts and all the five families will go after the Corleone family. However, the Corleone family is one of the five families, so he should have said that the other four families will go after the Corleone family.
When Vito Corleone shows Johnny Fontane out of his office, we see an extra walk onto the frame from the left, but as soon as she sees Vito, she quickly lets out a little smile and backs away, as if she was in the wrong place.
When Don Corleone is talking to the pastry shop owner during the wedding scene, the man is holding a small shot glass. As he is getting up to grab Don Corleone's hands, the glass is still in his hand but in the next shot it is gone.
After Vito Corleone's brush with death, Fredo sits next to the front of the car on the pavement and next to Vito's head. But following that, when pedestrians walk towards Vito, Fredo is gone, then he is back in the same place in the next shot.
Enzo (the baker) visits Don Corleone in the hospital after he is critically wounded. Enzo is holding a large bouquet of pink carnations and baby's breath. Later, when he is standing outside the hospital with Michael, the bouquet has been changed to a much smaller one with orange carnations.
When McCluskey is harassing Michael at the hospital, Michael's jacket changes. Michael's jacket is open a few inches near his tie as McCluskey is puling back his arm to hit Michael. After the cut his jacket is closed and straight when he gets punched.
The gun that Sonny gets from the drawer in the dining room when Clemenza comes to the house following the attempt on the Don's life, is in his belt, disappears when he throws Clemenza against the counters and reappears as he turns around after talking to his wife.
When Michael is telling Kay about Luca Brasi, she has a cigarette in her left hand which disappears and reappears between shots. A few seconds later, the cigarette is gone and Kay has a fork in her left hand which then jumps to her right hand.
When Michael gets in Sollozzo and McCluskey's car, we see that there is a long distance between the two men on the back seat and Michael on the front seat. However, in the next shot, with Michael in close-up, the two others appear just behind him.
When Michael reads the paper about his father's brush with death, he crumples it and then starts to run across the street. The paper is crumpled in his hand as a car passes in front of him on the street. After the car passes, Michael throws the paper down. When he does this, the paper is very smooth and neatly folded.
When Tom is talking to Woltz about putting Johnny into is new film, when they are standing by the door, the right side of Woltz and the left side of Tom are in light, but in a close up the same sides are completely in shadow.
The coffee cup Sollozzo drinks out of in the scene where Tom Hagen is held hostage is seen again at the hospital when Michael visits Don Corelone. When Michael looks into one of the staff rooms, the coffee cup is there next to the half-eaten sandwich.
When Michael returns to New York from meeting Moe Green in Vegas, two black sedans pull into the Corleone compound, with Michael and Kay apparently in the second sedan. The cut to the interior of the vehicle shows Michael, Kay and their son in the back seat of a two-door vehicle, not a four door.
When Tom Hagen is having dinner at film producer Jack Woltz's home, the butler fills Tom Hagen's half-empty wine glass. In the next shot, Hagen's glass is one-third filled and the butler is filling it again.
After Fredo yells at Michael for trying to negotiate with Moe Greene, we see a shot of Michael smoking. As Michael exhales, we see a cloud of smoke quickly disappear from his mouth as the camera splices to another take of the shot.
When Sollozzo is taking Michael to the restaurant for their conference, his car drives onto a bridge, where Michael sees a sign reading "To New Jersey", and he asks, "We're going to Jersey?", just before the car U-turns in mid-span. In fact, the only bridge between Manhattan (where they picked Michael up) and New Jersey is the George Washington Bridge, and the bridge on which the car is shown is definitely not the GWB. (It may be the Williamsburg or 59th Street bridge.)
The use of the title 'Don' is incorrect as the proper use of this term of respect is always attached to the individual's first name, not surname. Marlon Brando's character should have been addressed as Don Vito, not Don Corleone. Same rule would apply to the other 'Dons'... Barzini, Fanucci, etc.
The punch to Michael's face broke his cheek bone which gave him a permanent black eye (and caused his sinuses to continually run - hence the use of a handkerchief all the time) until he got back to America and had surgery to fix it (Freddie says, "that doctor did a good job.")
The exterior set-up shot for the summit meeting of all families is of the Federal Reserve Bank of New York. While this seems like an unlikely place for a "family" meeting, it's an indication of how high their influence reaches.
When Michael is moving Vito to a different room in the hospital with the help of the nurse, we can see that Marlon Brando instinctively moves his hand when it hits the door post. However he is conscious, hence his crying while Michael is holding his hand, just heavily sedated due to the pain inflicted by his gunshot wounds.
When the movie opens, Michael is a returning combat Marine Corps Officer (based on his uniform). Yet later when he decides to "make his bones" by killing the two men in the restaurant, he needs to be trained in the use of a handgun. As an Officer, he would have been fully trained and qualified in the use of a .45 automatic. Why did he suddenly lose his shooting skills?
During the sequences filmed in Sicily, Michael's broken-jaw make-up does not match the make-up used during the sequences filmed in New York. This is because Paramount Pictures would not pay the costs of sending makeup artist Dick Smith to Italy with the rest of the crew.
When Michael gets out of the car in front of the hotel in Las Vegas, he is with his brother, Fredo. However, it is clearly not John Cazale (Fredo) getting out of the car, but someone else (notice the hairstyle in the scene).
Outside the hospital, as McCluskey prepares to punch Michael, as the shot changes showing McCluskey (Sterling Hayden) punching Michael, it is clearly not Sterling Hayden throwing the punch as evidenced by the longer, brown hair of the man doing the punching (vs. Hayden's short, gray hair).
The goof items below may give away important plot points.
The stop sign in New England when Michael returns from Sicily (before his father dies in 1953) is red and white. Stop signs were yellow and black at that time and did not change to red and white until the mid/late-1950s.
Sonny dies in late 1948 or early 1949; however, he was listening to the 3 October 1951 radio broadcast of Russ Hodges calling the Dodgers-Giants playoff, a half-inning before Bobby Thomson's "Shot Heard 'Round the World," two years later.
Just before he is shot, Don Corleone shops for fruit at a shop. Cardboard boxes of Sunkist oranges in that shot feature graphics that weren't introduced until the 1970s. In 1945 most oranges were still shipped in wooden crates.
At the Don's funeral, the other crime family heads arrive in Cadillac models from the mid-1950s, several years after their own murders, which are said throughout the series to take place in either 1950 or 1953.
After Michael kills Sollozzo, there is a series of newspaper headlines. The last one is an article entitled "Syndicate Big Shot Vito Corleone Returns Home". In the corner of that paper is an "Index", which has a line beginning "TV/Radio". In 1945 or 46, there wouldn't be television listings, even in New York newspapers, as so few people owned televisions at that time.
When Don Corleone is talking to Michael, just before the Godfather dies in the garden, he asks Michael if he's happy with his wife and his children. Michael & Kay only had 3-year-old Antony at that time.
When Tom Hagen tells Don Corleone about Sonny's death, Corleone says "Consigliere of mine, I think you should tell your Don what everyone seems to know." Marlon Brando pronounces the G in Consigliere. Any Sicilian would know that the G in this word is silent.
Michael fires his gun twice at McCluskey in the scene. The camera is on Michael for the first gunshot. The cut to McCluskey after the first gunshot shows him to reaching for his throat and making gurgling noises , indicating he's been shot in the throat. In that same long shot, the bullet wound to the head appears after the throat reaction. For the second gunshot, the camera cuts back to Michael firing the gun, then cuts to McCluskey, where the forehead gunshot wound appears after and in response to the second gunshot.
When Don Corleone is shot at the fruit stand, Fredo stumbles out of the car, fumbling with a gun and lurching, nearly falling forward. The next shot, from overhead, shows Fredo walking steadily around the car toward the Don. The third shot, back at ground level, shows Fredo stumbling again.
While he instructs Michael how to behave after to kill Sollozzo and McCluskey, Clemenza has a cigarette in the mouth. From one shot to another, when Michael passes in front of him, the cigarette jumps to his left hand.
The death of Barzini: During the string of shootings during the baptism, Don Barzini (Richard Conte) is shot on the courthouse steps. In the medium close shot, the squib bullet-hits are clearly visible. In the long shot, however, Conte's stunt double tumbles down the stairs without any bullet holes on the back of his jacket.
When Tom Hagen is abducted by Sollozzo after Christmas shopping, it is clearly nighttime. In the next scene Don Corleone is gunned down and it is clearly daytime. Later Sollozzo tells Hagen that they hit the Don about an hour after they abducted Hagen.
During Vito's funeral, when Michael stands up to talk to Tessio, the face of Mama can be briefly seen under his arm, tinted orange-red and chewing gum. After Roger Ebert reported this in his "Movie Answer Man" column in 2001, Francis Ford Coppola and Kim Aubry investigated: they confirmed that Morgana King was not supposed to be in the shot, but had gotten into it by an accidental reflection in the optics, probably off a filter (hence the tint) in the matte box.
The opening cemetery shot of Vito Corleone's funeral procession shows two towers side by side in the distance which are incorrectly thought to be the World Trade Center towers. They are in fact smokestacks, complete with smoke, and are in nearly the opposite direction as Lower Manhattan and WTC.
When Cuneo is killed in the revolving door of the hotel the first shot breaks the glass in front of him but no blood squib appears on his shirt. It is not until the second shot goes off does blood appear.
The eyes in Khartoum's severed head have obvious cataracts (which are typically caused by old age and/or degenerative diseases such as diabetes). That is hardly what you'd expect to find in a champion stallion in the prime of his life.