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.
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.
When Naomi and Arthur enjoy their "first date" in the middle of Grand Central Terminal, darkness is seen outside the windows as if its the middle of the night, even though they were in bright daylight moments earlier outside on 42nd Street.
Near the end of the movie, outside Naomi's apartment, Arthur states "My mum's dead." It was his Nanny, Hobson, that passed away, but she was more of a mother than Vivienne ever was, and Naomi would know that. (This is also parallel to the original film, in which Arthur tells a drunk "My father died" after the passing of Hobson. Arthur's actual father was still alive and well in the film.)
Hobson: My Name is Lillian and I am an alcoholic. I'm rich, I'm fabulously rich. I'm also generous and kind hearted. My father died when I was young and my mother was absent most of the time. Is this an excuse for making a mockery of my life? Oh it all looks very wild from the outside, I once went to bed with three European Princesses at the same time but A, I cant remember anything about it, and B, apparently I vomited over two of them before losing control of my bladder on the third, oh yes all such fun. Until the fog parts and suddenly there's a hole so big that all the vintage champagne and all the bat mobiles on the world can't fill it. Then I'm all alone on my magnetic bed, wondering what venereal disease I've just caught.