During the brass band parade, multiple room air conditioners can be seen on the outside walls of the buildings. These were not common until after WWII, and would have been extremely rare during the depression era, especially in the Black neighborhoods of New Orleans.
In the opening segment where Stoner is been chased through the railroad yard. The two diesel-electric locomotives shown are from the late 1950s and contemporary with the shooting date of the movie c.1964. Dieselization of the US railroad system did not start until 1949.
Throughout the final poker game of the film, Hoyle poker cards with "shell back" are dealt by Shooter and Lady Fingers. When the man flips his jack of diamonds, a close-up of his cards shows a jack and a queen of diamonds in the standard style of Bee or Bicycle decks, even though we have seen a close-up of a Hoyle-style jack of diamonds before and the end credits display the man's final hand with Hoyle-style queen and jack.
When the Kid is playing a card trick with Christian's father, the deck changes positions between camera angles.
When the Kid is showing the trick to the father, he is wearing a coat. When the mother comes in to see the trick, the jacket is gone and nowhere to be found.
In the final hand, Lancey overlaps his exposed cards similar to a solitaire row, the queen of diamonds is the top card while everyone is discussing if he has the jack or not. A few seconds later, the cards are reversed and the queen is the bottom card.
In the opening card game of 5-card stud, the pot of money is shown at the dealer's left side of the table, then after a brief shot of The Cincinnati Kid's face, it is shown in the center of the table, barely in view. (at about 4:14)
When Pig goes after Lancey for taking all his money, The Kid grabs him by the shoulder to restrain him and calm him down. In the long shot of the table and the players, The Kid's hand is on the back of Pig's shoulder. But when the shot changes to a close-up, The Kid's hand is in front of Pig's shoulder.
When "Shooter" is dealing cards in the 5-card stud game rather than dealing the first card to the player to his left (Howard) it appears that he skips him and deals the first card to the player to his left. This is in fact normal practice for card tables to "rotate deal" so that every player gets a chance to be the first to bet. It is the job of the dealer to keep track of the positions, and that is why it is common to have a "dealer button" that passes to the left.
When the Kid is accusing Shooter of cheating by dealing him winning hands, Shooter begins to deny it, and the Kid grabs Shooter by the lapels and bangs him into the door. When he does that, the whole door and jamb and the wall beside it visibly shake and move, showing that the wall is definitely not a real wall.
The goof item below may give away important plot points.
In the climactic hand, when the Kid first arranges his 4 'up' cards at the end of the hand, the ACES are bracketed by the 10s. Yet when he reveals his hole card at the end, the cards have switched and now the ACES bracket the 10s.