The microphone on the talk show host's desk is a Shure Super 55. In every scene, it is pointed down at her desk, rather than at the host.
Katherine has won at least eight Emmys over nearly 30 years, and presumably none in the past decade. Yet someone mentions she lost the first time to John Oliver, whose own show didn't begin until 2014.
During her acceptance speech for American Humor, Katherine makes a joke about foreigners stealing Americans' jobs and asks if Martin Short is dead. Martin Short was born in Canada.
In a scene late in the movie, Molly (Mindy Kaling) calls Tom (Reid Scott) "Dan" - possibly an homage to the character he plays on Veep.