When Elliot is on the beach, as the devil walks by with two dogs she refers to them as Dudley and Peter, which is a reference to Dudley Moore and Peter Cook - the stars of the original Bedazzled.

Not a mistake but something clever. When the Devil was a schoolteacher, the first equation on the board was Fermat's Last Theorem (X to the Nth + Y to the Nth = Z to the Nth for N is greater than 2). It was proven in 1995 that there is no integer solution to this equation; exactly the kind of problem the Devil would give to an Algebra class, but not really expected in your standard Hollywood film...

When Elliot returns home during the wish where we find out he's gay, his boyfriend mentions the movie The Pajama Game, which was directed by Stanley Donen, the director of the original Bedazzled film.