While Simon has enjoyed a great deal of financial success on Broadway for many years, critics have generally been disdainful of his work. Brighton Beach Memoirs is regarded as the play which changed that. Many critics believed the play was the first time Simon successfully combined comedy with serious themes, and many expressed hope that Simon would finally be taken seriously by scholars. Not all critics agreed on the work's merit, but Simon did receive some of the best reviews of his career for Brighton Beach Memoirs.

T. E. Kalem of Time wrote: "Without slighting his potent comic talents, Simon looks back, not in anger, remorse or undue guilt but with fondly nourished compassion at himself as an adolescent in 1937 and at the almost asphyxiatingly close-knit family around him.’’ Frank Rich of the New York Times concurred, stating ‘‘Mr. Simon makes real progress towards an elusive longtime goal: he mixes comedy and drama without, for the most part, either force-feeding the jokes or milking the tears. It's happy news that one of our theater's slickest playwrights is growing beyond his well-worn formulas of the past.'' But Rich went on to argue that the play is not as good as it could be. He called it superficial, and criticized its skirting of deeper issues. Rich also felt that the character/narrator Eugene was too glib. Rich's colleague at the New York Times, Walter Kerr, disagreed, writing: ‘‘The shrewdest of Mr. Simon's ploys, and very probably the best, is not simply to have made the boy hilarious in his likes and dislikes, his comings and goings, his sexual gropings. Mr. Simon lets us watch the comic mind growing up.’’ Kerr, though, felt the second act faltered in part because "we tend to lose Eugene'' in favor of the rest of the family.

Critics who disliked the play often focused on the weakness of Eugene. Jack Kroll, writing in Newsweek, said that Simon's "young hero, Eugene, wants to be a writer but Simon gives him so much dialogue about masturbation and naked girls that it gets unfunny and embarrassing.’’ But the reviewer conceded, like many other critics, that "There are moments of tenderness and insight.’’ Catharine Hughes in America agreed. She wrote: "His youthful narrator almost always steps in to diffuse seriousness with a facile, albeit usually funny, remark. After a time, this becomes too predictable as a device.’’

Other critics found Brighton Beach Memoirs as a whole to be problematic. The Nation's Richard Gilman stated, ‘‘The first act contains the usual complement of more or less amusing episodes and funny lines. But the second act turns serious. That is to say, Simon wants to be a dramatist and so devises some hokey stuff about family life in the Depression, the growing menace of fascism, intergenerational conflict, and youth's awakening to sex. It's all obvious, derivative and flaccid.’’

Many critics who criticized the play often focused on Simon and his background. While Simon says that he based Brighton Beach Memoirs on his adolescence, he did not intend it to be wholly autobiographical. None of the play's dramatic incidents actually occurred in his own youth, though he experienced many family difficulties. Critics suggested that Simon could have written a better play if it had been more autobiographical. Kroll wrote,"In an interview Simon talks about his 'extremely painful' childhood, how he lived with a pillow over his head to block out the bitter fights of his parents, how his father would leave for long periods, how he was abused as the only Jewish kid in school. Why isn't this in the play?...