The phone booth that Wade Wilson changes in has "Nathan Summers cumming soon!" written on it. Nathan Summers is the real name of Cable, who will appear in Deadpool 2 (2018).
The phone booth scene is a homage to Superman, often receiving homages as using a phone booth to change between Superman and Clark Kent. However, specific examples of the phone booth as a changing room rarely occurred, particularly following the 1940's, when phone booths started to have transparent glass or plastic sides. Wooden phone booths seemed available in the 1940's, per The Mechanical Monsters and The Bulleteers. The Superman (1978) score plays as Wade runs to the phone booth to change. Inside the phone booth the word "hope" is seen; the Superman S shield is the Kryptonian symbol for "hope".
The musical score played towards the end of the short is the theme from the movie True Romance (1993).
As Deadpool runs across the street to where the man is laying, a poster for Firefly is seen, another Fox production in which features Deadpool (2016) actress Morena Baccarin.