While sulking in his Batmobile after Hobson gives him an aspirin and vitamin, Arthur played by Russell Brand, scrolls through his phone to look for Naomi's number and we briefly see Katy Perry, Brand's then-wife, listed as a contact.
Naomi mentions that her favorite place to shoplift is Bergdorf Goodman's department store. When we meet Linda, Arthur's love interest in the original Arthur (1981), she is shoplifting a tie from that store.
In order to see the dedication in Naomi's book, Arthur moves a pop-up moon over a Manhattan skyline scene. This is a tribute to the line "If you get caught between the moon and New York City," in Christopher Cross' "Arthur (1981)'s Theme" song.
The table saw that Burt Johnson (Nick Nolte) threatens Arthur with is a real saw. It is called a SawStop and is designed to instantly apply a break and stop the saw blade within milliseconds of coming in contact with a human appendage. However, it works more by detecting the natural electrical current in the human body and not so much by moisture as stated in the movie.