Continuity mistake: During the dinner scene at Tom's, a couple of shots before Tom's phone rings and he goes to answer it, Nick's wine glass is about half full. After Daisy leaves to go to Tom and the shot cuts back to Nick, the level of wine in his glass has notably decreased, without him touching it. (00:09:50)
Continuity mistake: As Gatsby and Nick overtake a truck on a bend, he swerves in front of the truck to avoid an oncoming car. In the very next shot, he is not in front of the truck, nor is there an oncoming car. (00:36:30)
Continuity mistake: When George kills Gatsby, Gatsby falls into the pool with his arms by his side, but from a reverse angle, his arms are raised in the air. (02:02:35)
Continuity mistake: When Gatsby points out to Tom that his house is across the bay, there is then a shot of the house from Tom's view. The shot returns to Tom where we can see nothing around the top few inches his abdominal area. In a side angle of him, his cigar has suddenly appeared there. (01:28:35)
Continuity mistake: While Gatsby drives with Nick he takes his hat off and waves it, then it's back on, and then back to the previous angle of him waving it.
Factual error: In the beginning of the film, when Nick flashes back to 1922, he mentions that the buildings were taller, and a shot of the Empire State Building is shown. But construction on that didn't even start until 1931. Even the Chrysler Building didn't start construction until 1929.
Continuity mistake: At Gatsby's second party, a band starts playing. The shot cuts to Gatsby, Nick, Daisy and Tom watching them. In this shot, Gatsby and Tom are a foot or two away from each other, but in a sudden close-up of the two, they are suddenly closer together. (01:12:30)
Continuity mistake: At the Plaza Hotel, Gatsby loses his temper and a strand of hair falls on his forehead. He takes both hands to button his jacket and when the angle changes his hair is brushed. His hands were too busy for him to do it between shots.
Continuity mistake: Meyer meets Nick and places his hand on his shoulder. A frame later Meyer is standing sideways, several meters away from Nick.
Audio problem: When Gatsby and Nick are in his car driving to meet Wolfshime, in wide shots you can see that what Leonardo DiCaprio is saying does not match his mouth's movements.
Factual error: The movie takes place in the summer of 1922. They played Rhapsody in Blue, which wasn't written till 1924. The bandleader is obviously Cab Calloway. Cab Calloway's first recordings with the Missourians weren't until 1928. "Oh! You Have No Idea" also wasn't recorded until 1928, and it was sung by Sophie Tucker, not Josephine Baker (although they do credit Ms. Tucker in the final credits).
Factual error: Trains of various types appear in several shots but the trains shown - likely all CGI - are completely unlike any trains that were in use in New York in the 1920s or in any other era. They appear to be based on Australian prototypes and their design differs significantly from American trains.
Continuity mistake: When Nick meets Gatsby at the party, the amount of confetti on his shoulder and hair changes between frames, sometimes appearing or disappearing on the same spot, depending on which angle is shown.
Continuity mistake: When the doctor tells Nick to write the story, the pen's position differs between the close-up and wide angles from being in a 5 o'clock or 12 o'clock position.
Continuity mistake: Just after Gatsby asks Nick his opinion of him, there is a cut to a low angle of him driving. In the shot from behind the car, the number plate is on the right hand side of the back of the car. This is only visible for a fraction of a second, so you have to be quick when you look at this. 2 shots later, the number plate has moved to the left side of the back of the car. (00:36:10)
Continuity mistake: During the meal where Gatsby is about to say that he and Daisy are in love (before the trip to NY), Daisy's fringe is messed up in the wide angles, but perfectly brushed in the close ups. This changes back and forth.
Factual error: The "French" phone shown as they talk about the intrusive unwanted guest calling Tom wasn't invented until about the mid-30's. In 1922, you still had to hold the candlestick phone in one hand and talk into the mouthpiece while holding the earpiece up to your ear.
Continuity mistake: Right before Myrtle is run over, she runs down the stairs, hair messed up. She stops for a brief second where the angle changes to a close-up, when her hair style changes completely.
Revealing mistake: When Gatsby and Tom are racing (a CGI achieved scene), note that the passengers' hair barely moves. (01:32:00)
Continuity mistake: After Gatsby tells the story of how he met the sailor there's a blue shirt on the bed which disappears when he exits the library.
Chosen answer: The song is "Back to Black" by Beyoncé (Feat. Andre 3000).