Hank references a famous internet cat that jumps into boxes. This is a reference to Maru. As of September 2016, videos featuring Maru have been viewed over 325 million times, at the time a Guinness World Record for YouTube video views of an individual animal that has since been broken.
When the Hamburgler bangs his giant head on the prop doorway on the soundstage, it is a visual nod to the Star Wars meme where helmeted characters such as Stormtroopers or Boba Fett bang their heads because the helmet blocks their vision. Liz Lemon is of course a giant Star Wars nerd/fan.
Frank's trucker hat reads "Emoticon Illiterate".