The scene involving Lenny Bruce on Steve Allen's show, is a recreation of his actual appearance and routine, though here it's cut shorter than it was. In real life he performed the "kids huffing glue, as "George Macready" bit that is seen in the Mrs. Maisel pilot. The Steve Allen episode aired April 5, 1959, months before it supposedly happens in this show, and can be found online.
A poster for Alfred Hitchcock's 1958 film "Vertigo" hangs in a prominent spot in Joel's office at the garment factory.
Actually not all of the material Lenny performed on Steve Allen is shown but when Lenny performs in a club earlier in the episode he uses the material not shown later.
The model for superstar crooner Shy Baldwin is almost certainly Johnny Mathis. But although the character Shy looks and sounds like Mathis, in his career, real-life Johnny never did record the hit song "Younger Than Springtime" from the famous Broadway musical and film South Pacific (1958).