Barnes had significant influence in reviewing new Broadway productions and evaluating the international dancers who often perform in New York City.

[1] In 1967, many of his duties as drama critic were given to Walter Kerr, as the paper's editors were concerned by the level of influence amassed by one person holding both roles.

"[5] The Daily Telegraph noted that Barnes sometimes wrote four reviews a day, possibly because New Yorkers were "greedy for his brand of pithy English open-mindedness."

The English writer was particularly good at identifying American talent and introducing artists like George Balanchine and Martha Graham to London audiences.

"[7] Goldman gave the following reasons for this:[7] (1) He has no ear for American speech; (2) he cannot deal with American drama; (3) he prefers, in all ways, English theatre to American theatre; (4) he would find it not at all ignoble if Broadway were to become primarily an importing agent; (5) he prefers ballet to theatre; (6) he is a smart ass; (7) he enjoys glorifying himself publicly through his position; (8) he changes his opinions constantly, which is certainly the right of free men, but not so helpful when the life or death of a play is based on a critic's having the courage to say what he thinks now, not a month later in a ballet column; (9) he has little interest in learning the financial aspects of Broadway, to which he is central.Barnes was married four times, with the first three marriages, to Joyce Tolman in 1947, to Patricia Winkley in 1958, and to Amy Pagnozzi in 1985, ending in divorce; his fourth marriage, to Valerie Taylor, lasted from 2004 until his death.