When the prisoner arrives at the prison in the opening scene it is pouring rain outside. He exits the vehicle and walks inside yet a closeup of his shoes show they are completely dry.
When looking over Marlowe's novel, Lawson, as narrator, notes that a "murder" refers to a group of crows, like an "exaltation of doves." However, an exaltation refers to larks, not doves. Doves are either a "dole" (or "dule") or a "flight."
At 0:02:12, you see that the belly chains and leg irons are on wrong. The keyholes are always positioned facing away from the hands (up the arm) and toward the feet (down the leg). This restricts the inmate's ability to access them.
When Dubose receives the book in the mail and flips the cover open to see the autograph from Lawson you can see that all the words from the book cover on the inside of the book are complete gibberish. None of them make sense in any recognizable language.
This addition is all in fun.
When Det. Dubose feeds his cat, the cat is "surprised", with the canned food presented before him.
The cat would have been bothering him as soon as he opened the can.
When the police close in on Lawson in his house (around 1:03:00 into the movie), Officer Phillips enters the bathroom, notices steam on the mirror, and then uses his communications radio to say "One Park 14, com one" while holding the send button on the radio. Then he says "He's here" but doesn't press the send button down on the radio until he's almost finished talking.
As a prominent New Orleans attorney with court dates and client meetings, it would be virtually impossible for Lawson Russell not to have a viable alibi for any of the five murders that occurred across multiple states.
When Russell is holding the two guns, he is panicked by the thought that his fingerprints are on a murder weapon. A halfway decent defense lawyer would also realize that there would be no gunshot residue on him.