This is one of the few instances when a movie was released while the Broadway play was still running.
The original Broadway production of "Mary, Mary" by Jean Kerr opened at the Helen Hayes Theater in New York on March 8, 1961, later moving to the Morosco Theater, for a total of 1572 performances, making it the longest-running non-musical Broadway show of the 1960s.
The picture behind Doug's desk is that of actor Monty Woolley who died the same year the film was released.
Barry Nelson, Michael Rennie, and Hiram Sherman repeat their roles from the Broadway production: Debbie Reynolds assumes Barbara Bel Geddes' Broadway lead role,
Dirk says an Indian head looks like Jack Warner. Presumably Jack L. Warner, the head of the studio, approved of the joke.