The Title (Situational Irony)
"The Great Gatsby" implies that Gatsby is a successful and accomplished man, which he is. However, his methods for achieving success and gaining money are corrupt and illegal. Furthermore, he is a poor man who has amassed his wealth for the sole purpose of running away with a married woman. By the end of the film, he is dead in the pool, wrongfully killed by the vengeful Wilson, and no one attends his funeral. By all accounts, Gatsby's life and ultimate fate is anything but "great." Having had his reputation tarnished, his dreams shattered, and his life taken from him, Gatsby ends the film in a hard place. In Nick's eyes, however, he is still great. Nick says of the old-money crowd with whom he has been associating, "They're a rotten crowd!" then adds, "You're worth the whole damn bunch put together." While Gatsby has a complicated biography, and his personality is full of flaws, at the end, Nick decides to call his manuscript The Great Gatsby.
The Final Phone Call & Gatsby's Death (Dramatic & Situational Irony)
There are multiple layers of irony in the scene of Gatsby's death. At the end, Gatsby waits patiently for the phone to ring, expecting Daisy to call him so that they can make arrangements to run away together. While the audience knows that Daisy is likely to stay with Tom, having seen her conversation with him after the accident with Myrtle, Gatsby does not know about Daisy's reservations about running away with him, and assumes she will call him in the morning. This contributes to a sense of dramatic irony, because the viewer knows more than Gatsby about Daisy's likely decision. When the phone rings, Gatsby looks over at it, delightedly assuming that it is Daisy, but is suddenly shot dead by George Wilson. His murder by George Wilson is ironic and tragic on multiple levels. Firstly, it is ironic because just when Gatsby believes he is being contacted by his lover with whom he wants to run away, he is killed. Secondly, it is ironic because while George Wilson believes that Gatsby was having an affair with Myrtle—and this is the story that gets proliferated to the press, following Gatsby's murder—the viewer knows that this is not the case, that Gatsby is blameless; Tom was the one having the affair with Myrtle, and Daisy was the one who hit her with the car. Finally, to add even more irony to the situation, the phone call that Gatsby receives just before his murder turns out to have been Nick calling to check in with him, not Daisy. Thus, Gatsby died still believing that Daisy wanted to run away with him.
Gatsby's Funeral (Situational Irony)
While he was alive, Gatsby threw many lavish parties, which attracted all different kinds of people. As we see in the party scenes, they flooded the hallways of the mansion and filled the grounds. Gatsby's name was magnetic and mysterious, and hundreds of people would show up to drink his alcohol and fill his house like friends. However when Gatsby dies, no one shows up to his funeral. The irony lies in the fact that in the world of the film, people are more than willing to attend a lavish party than they are to attend a funeral for the man who provided the parties. The funeral shows the empty shallowness of the social worlds shown in the film.
Tom Buchanan's Belief that He is Better than Gatsby (Situational Irony)
A potent irony lies in the fact that Tom Buchanan is a brutish and violent misogynist, openly cheating on his wife and striking Myrtle in the face at the party in her apartment, but he ends up wielding more romantic power than Gatsby. He deems Gatsby unsuitable for Daisy, and denigrates Gatsby's character based on class. Ironically enough, even though Tom comes from old money, he behaves in a completely classless and irredeemable way himself throughout the film. Tom's hypocrisy and investment in his own good breeding is ironic because he is such a lout. Furthermore, while Gatsby has been involved with unethical business dealings, he behaves more ethically towards Daisy. Gatsby's deep love for Daisy is not enough to win her, however, and in another ironic twist of fate, the philandering Tom Buchanan wins out.