In the beginning of the game, while accessing the "interwebs" to achieve the "Playing with Deadpool's Junk" trophy, Deadpool complains about persistent friend requests from "Ryan". This is a nod to Ryan Reynolds, who plays Wade Wilson/Deadpool in X-Men Origins: Wolverine (2009) and later in Deadpool (2016).
In the beginning of the game, Deadpool complains about not finding his autographed comic book, "New Mutants" issue number 98. This was the comic in which Deadpool first appeared.
In the beginning of the game, when Deadpool is editing the script, if you look closely, the script entails all of what he is saying while doing this.
After falling from White's tower and landing back in the sewer, off the main path you'll find a hole in the wall. If you head in you will find a pizza box with a slice missing and a ninja sai. This is a homage to the "Teenage Mutant Ninja Turtles."
When Deadpool is about to kill the second clone of Mr. Sinister, his voices tell players not to complain that Rogue suddenly lost her ability to fly by saying "Yeah, she flies in OUR game!". This is a reference to the fact that in most animated series, movies and games featuring Rogue (except X-Men (1992)) she doesn't have the flight ability she has in comics.