Although the letters POE and OPE are shown reflected in the mirror in reverse, the writing on the "We aim to please..." sign on the same wall is not reversed. Later, when the Biker breaks down the door, you can see that the sign is actually printed in reverse lettering.
Randall 'Tex' Cobb was not familiar with riding motorcycles prior to filming. While shooting the scene where he rides up to inspect the hole where Evelle and Gale had escaped from prison, he actually crashed into the hole on one of the takes.
The lullaby that Ed sings to Nathan, Jr. is the song "Down in the Willow Garden", a folk song about a man sentenced to death after brutally murdering his fiancee.
The cigar-smoking bird tattoo was originally the logo of Clay Smith Cams in 1950s, a company making high performance engine parts. The logo, with the trademark clenched cigar, represents Smith himself and is known as "Mr. Horsepower". Smith closed the business in the 1960s and the logo was adopted by what is now Tenneco for their Thrush muffler line.
The prison counselor at the beginning of the film wears a Chai on his necklace. Chai is a Hebrew word and symbol that means "life," and is pronounced as if you were saying "hi" in English. Nicolas Cage's character "H.I." is called "Hi" throughout the film.
At the end of the sequence where H.I.'s dream of the lone biker forms into the reality of Mrs Arizona discovering she is one baby short, the camera skims along the ground and jumps a child's bike, a car and then a fountain, before shooting up the ladder into the bedroom. This sequence seems to be a reference to the condensed career of motorcycle daredevil Evel Knievel, who jumped bikes, cars, buses and then spectacularly crashed after jumping the fountain at Caesar's Palace, Las Vegas.
The trivia items below may give away important plot points.
The shot where Evelle and Gale stop just before hitting the car seat with the baby in it, was filmed in reverse, with the car driving away from the seat.
While many reviews refer to Randall 'Tex' Cobb's character Leonard Smalls as a "Harley-riding biker," the motorcycle in the movie is in fact a Honda Shadow that has been subjected to the "Rat Bike" treatment along with some extra flame-emitting plumbing. The Shadow is slightly smaller than a Harley Big Twin, which would give Cobb's character a bit more stature than he already has. One must also assume that since the bike is trashed near the end of the movie, it saves the production company a few coin.