Gatsby's car is a Duesenberg. The model A would have fit the era of the movie (the first Duesenbergs were made in 1921), but the model used in the movie was an SJ model, which didn't start production until 1929.note The car was actually a Duesenberg II, an homage model that started production in the late 70s.
New York City didn't have that many skyscrapers in the 1920's
Anti-Hero: Leonardo Dicaprio plays up Jay Gatsby's dark side, with him nearly punching Tom (in the novel, he merely argues with him), and ordering a rogue gangster to beat up at a party by his gang. This makes the suggestion that Gatsby "killed a man" even more probable than in the novel.
On the other end, Tom and Daisy are made to be a bit more sympathetic instead of the callous jerks they amounted to be in the novel.
Art Deco: The movie's titles in the opening and in most of the promotional material.
Author Avatar: Nick is intended as this for F. Scott Fitzgerald. Tobey Maguire was likely cast because of his resemblance to Fitzgerald.
Gold Tooth: Unlike most examples Meyer Wolfshiem wears his on his tie in addition to his infamous cufflinks.
Dawson Casting: Carey Mulligan (28) as as the 23 year old Daisy and Leonardo Di Caprio (38) as the 32 year old Jay Gatsby, who also play those characters in flashback when they are 18 and 27, respectively.
Downer Ending: Tom Buchanan's mistress is run down by Daisy in Gatsby's car, for which he takes the blame. As this goes on, Buchanan tells Myrtle's husband where Gatsby lives. Gatsby goes swimming as Nick goes to work, but, while he's gone, Gatsby is murdered by the husband, who then commits suicide. Daisy and Tom pack up and go, leaving Gatsby to take the blame for Myrtle's murder. Nobody attends his funeral but Nick, and his reputation is completely destroyed. Nick then loses faith in the world and commits himself to an Asylum. Inspiring stuff.
Hope Spot: Swimming in his pool, Gatsby awaits the call of Daisy, anticipating that she will agree to run away with him. It is clearly shown that Daisy does indeed reach for her phone. Back at his mansion, Gatsby hears the ring and regains hope. But after Gatsby is shot, the audience sees that Daisy had backed away and that it was really Nick, at work, who was trying to reach Gatsby.
How We Got Here: The framing device is Nick explaining the source of his depression and disillusionment to his doctor at a sanitarium he's checked into following the events of the summer.
Kissing Cousins: Brought up humorously by Daisy when she visits Nick and discovers how his house is full of flowers courtesy of Gatsby, and murmurs that he must be in love with her.
Large Ham: Joel Edgerton has his moments as Tom Buchanan, particularly in the scene where he confronts Gatsby about his affair with Daisy and proceeds to mock him about his upbringing, complete with an almost cartoonishly Evil Laugh.
Leitmotif: Every time the green light at the end of Daisy's dock is visible onscreen, even when it's out of focus, the background music has the same note swelling in time with the light's pulse.
Pop Star Composer: Jay-Z contributes to the score, and is also one of the film's executive producers.
Promoted to Love Interest: In the novel, Nick and Catherine at Myrtle's apartment just talk. In the 2013 film, she immediately flirts with him and they share passionate kisses, before eventually having a one-night stand.
Relationship Compression: Nick's affair with Jordan Baker in the novel is compressed out of existence. He does try to pursue her and finds himself implicitly rejecting the chance of a relationship at the end, whereas in the book, they mutually break up.
As revealed by deleted scenes, the relationship between Nick and Jordan was initially in the film.
Retraux: The film opens and ends with a grainy footage of the credits while jazz music plays, making it look like a film from the 1920s.
Right Through the Wall: Nick has an uncomfortable moment when Tom drags him along for his rendezvous with Myrtle.
Standard Snippet: Johann Sebastian Bach's Toccata and Fugue in D minor, during the intro to Gatsby's party. Played on screaming jazz trumpet before transitioning into standard organ, as played by Ewing Klipspringer ("dubious descendent of Beethoven").
And then Gershwin's Rhapsody in Blue standing in for "The Jazz History of the World," doubling as Diegetic Music for The Reveal of Gatsby's identity.
Third Wheel: Nick finds himself as the third wheel in Gatsby and Daisy's affiar and Tom's affair with Myrtle.
Trailers Always Spoil: Gatsby's in bed with Daisy in the very first trailer; if you read the book they also include Daisy saying "You (Gatsby) always look so cool", which is practically a love confession in front of Tom; there's also a scene that might be George Wilson going for his gun. There's also a bit in the second trailer where Myrtle is struck by the car.