Both the arguments between husbands and wives and the drunk's car accident are Fitzgerald's way of introducing his themes and foreshadowing what is to follow. Let's look at the details that support this.
One theme of the novel is adulterous relationships, which we begin to realize more fully when we see Tom and Myrtle and later, when we see Daisy and Tom. The scene in which the couples argue is a precursor of this, since it appears that the basis of the arguments of the married couples is that one partner was having too much fun with someone else of the opposite sex, which we learn, for example, when one man is "talking with curious intensity to a young actress," (56) and his wife appears to drag him away, or when a wife says,"Whenever he sees I'm having too good a time he wants to go home" (56). These are people who are "fooling around," however innocuously, and while we might not consciously register this theme, somehow, it is not a surprise when we see the main characters so indulging.
Another theme of the novel is carelessness, the carelessly of the wealthy, which we learn more and more about as time goes on, but which we get a hint of in the carelessness of the drunken driver and his passenger. These are careless people, not on the same scale as Daisy and Tom, certainly, but nevertheless, people who are not exercising any consideration for anyone else, counting on someone else to clean up after them.
Finally, the fact that a car accident is central to the novel, the culmination of carelessness and adultery, really, strongly suggests that this first car accident is meant to foreshadow the next car accident. The drunks in this scene get off fairly lightly, but the stage is set for later on, when a car accident costs both Myrtle and Gatsby their lives.
In spite of the fact that this novel flows so easily, as though it all just happened, Fitzgerald was a thoughtful and careful writer, crafting all of his scenes quite purposefully. This is one reason this is one of the greatest of American novels and the reason it has to be read many times to gain an appreciation for Fitzgerald's magnificent craft.