Though it's never named in the film, in Richard Yates' source novel, the play April acts in (apparently badly) is Robert E. Sherwood's "The Petrified Forrest," written in 1935. In the play, the main female character, Gabby, dreams of leaving what she sees as a humdrum existence in the U.S. to move to France, just as April does.
The song that was audible throughout the main trailer was "Wild Is the Wind," written by Dimitri Tiomkin and Ned Washington and performed by Nina Simone. The song did not appear in the actual movie at least in part because it was not released until 1957 (two years after the main setting year of this film). Johnny Mathis was the first singer to record it (for the movie Wild Is the Wind (1957)) and it was nominated for a Best Song Oscar. Nina Simone's recording was made in 1966.
The second time Kate Winslet has been in a movie where she makes love in a vintage car and someone's hand hits the window and slides down it in the throes of passion. The first time was Titanic (1997).
Some scenes in the US and International trailer were not included in the final cut of the movie, such as the scene of Frank's "Nothing's forever, right?" line and the scene with Helen showing the Wheelers their soon-to-be home.
The trivia items below may give away important plot points.
It is noted above that Kate Winslet, Leonardo DiCaprio, and Kathy Bates all appeared in Titanic (1997), but the character interrelationships here are almost exactly the inverse. In Titanic (1997), Winslet and Dicaprio are members of different classes but with similar values, and their love proved stronger than society's rules. In this film, they are both middle class but with different priorities imprinted upon them by society, and it is society's pressure that causes their fundamental schism. In Titanic (1997) Kathy Bates' character is a rich person with commoner values who approved of the main character's dreams and believed the rules of society were ridiculous. In this film, Bates is a middle-class suburbanite who puts on airs of "propriety" and promotes the oppressive rules of society to such a degree that she alienates her own son and hypocritically "never liked" her good friends the Wheelers after their scandal.
In 1955, the year most of the movie is set, abortion was illegal throughout the US. It remained illegal in most states until Roe v. Wade in 1973 (see also the trivia for Dirty Dancing (1987)). In Connecticut, it was also illegal to buy or use any form of contraception, until Griswold v. Connecticut in 1965. One of Frank's work friends jokes that April's pregnancy was the result of a faulty prophylactic, but it would have been illegal for the Wheelers to use any form of birth control. Since Frank worked in New York, he could have brought birth control there, but its use in Connecticut still would have been illegal. In the book April comments that she felt her diaphragm was loose the night they conceived, and that she had to go out the next day to buy a replacement.
There are two scenes of on-screen sexual intercourse. In both instances, the man climaxes and the woman does not. A third scene (the secretary) only references the act, but still communicates that the man's satisfaction was the priority.