When Clarence is singing to the waitress in the restaurant, there is a picture of Susita on the wall. When seen at a distance, her head is tilted to the left, but in a closeup, her head is vertical.
While Joe Brady is sitting at the bar as the bartender keeps feeding him glasses of whiskey, he drinks the first and second glasses while talking to Clarence. The barkeep slides him a third glass, then a fourth. However, he never drinks the third glass. It simply disappears.
At the beginning of the fantasy sequence, Joseph Brady falls into a tunnel. When he gets up, there is considerable dirt on his white pants. A few seconds later, when he leaves the tunnel, his pants are clean again.
The Navy band is in a narrower position when they are shot closeup in spelling "NAVY" than they are when they are in the next long shot (as seen by their position adjacent to the painted lines on which they are standing).
The little beggar girl looks twice at Susan's picture while Joe is standing in front of the restaurant.
During the finale, the entire audience is wearing blue uniforms, yet the Navy orchestra members are all in whites. The change of uniforms is seasonal; they would all be in the same color.
When the sailors take Donald home, he states that the door is locked, but the policeman exits via the locked door. However, it is common for house doors in the USA to be lockable to the outside only.
When Clarence Doolittle sings "Brahm's Lullaby" to Donald Martin, he turns off the the overhead lamp. A split-second later, a light is turned on to simulate moonlight in the background window.
During the "Spanish Number", the bandit needs to swing up to the roof across from the wall he is on. There are two red curtains hanging nearby to the right. He grabs the one on the left and climbs higher on the wall. As he does, the upper end of the curtain moves more to the center and elevates by about ten feet, allowing him to swing across.
During the opening sequence, the Navy band is supposed to be standing on the deck of an aircraft carrier. As the camera pulls back, it is obvious that most of the deck is simply painted on and that the "deck" ends about twenty feet in front of the band. Additionally, in some widescreen prints of the film, the vertical edge of the painting and the studio wall behind it are visible at the right-hand edge of the screen for about two seconds before the camera angle changes.
After singing the lyric "she belongs to you and you and me" during his performance of "If You Knew Susie", Clarence briefly relaxes his hands and stops playing the piano, but the piano accompaniment on the soundtrack continues uninterrupted.
Shadow of the camera on the closet door.
(At around 91 minutes) The shadow of a crewman's head is clearly
seen moving around on the side of the piano.
(At around 68 minutes) The shadow of a boom mic is seen moving
downward on the sidewalk just behind Gene Kelly.
(At around 14 minutes) The shadow of a boom mic is seen moving
downward on the doorway just above Frank Sinatra.
(at around 1h 35 mins) The boom mic's shadow can be seen behind Joe, following him when he's lowering.