Cheryl's flip book comic is a reference to the kidnapping of Charles Lindbergh Jr., infant son of Charles A. Lindbergh and Anne Morrow Lindbergh.
The tune that various characters hum is from Gioachino Rossini's William Tell Overture. It was also used in numerous Looney Tunes cartoons when a dawn or sunrise is depicted.
Archer mentions "Le retour de Martin Guerre". This was a famous case of impersonation in a small village in 16th century France, where an impostor, remarkably similar to local man Martin Guerre, impersonated him for three years. When the real Martin returned from abroad after serving as a soldier, the impostor had deceived everyone, including his wife, and had successfully inherited Martin's possessions and fathered two children. The trial lasted several years, and although real Martin won, several witnesses could not distinguish them. As Lana mentions, one key piece of evidence was the size of the man's feet.
The repairman outside the elevator in Archer's building, Mr. Ford, as well as the references to slide shows and Wendell T. Stamps all come from Adam Reed's previous project, Frisky Dingo (2006).