Actually Timmy couldn't wish for a magic hat to help his dad do magic. When Mr. Crocker announced that he will cancel other shows and declare Timmy's Dad is the winner, technically the wish made Timmy's Dad win a contest. There should have been a contradiction to this because it is against Da Rules for a wish to win any contest.
This is the second episode to be a play on the words Abra-Cadabra, the first being Abra-Catastrophe!.
This episode aired 11 years after Where's the Wand?, one of the first episodes of the series.
The Statue of Liberty has a different appearance when she came out of Mr. Turner's hat compared to her other appearance in That Old Black Magic.
Criss Angel - Mr. Turner's appearance and his final act are references to Criss Angel. As well as he says "Brain Freak!" after he escapes from the box, which is a reference to Criss Angel saying "Mind Freak!".
Harley-Davidson - The Dadbra-Cadabra commercial parodies a Harley-Davidson Motorcycles commercial.
Leonardo DiCaprio - Mr. Crocker's disguise name "Denzel DeCaprio" is a spoof of the famous actor's name, Leonardo DiCaprio.
Harry Houdini - When Mr. Turner says "I'm going to become the next Houdini!", it is a reference to the famous British magician.
Mr. Turner mispronouncing "DeCaprio" (DeCapuccino, DeCaffinated, etc.).
One of the people who saw Mr. Crocker as a fairy didn't have arms.
Mr. Turner can't attract screaming fangirls that easily. To attract fans, he must perform more. But he got screaming fangirls before he hit it big.
When a man raised his arm with a bag to capture Crocker, his arm goes behind his body.