Continuity mistake: In the scene where Amelia is driving the truck full of policemen to the scene of the second (Mrs. Rubin) murder, the shot changes a couple of times before it settles looking through the front windscreen at Amelia. Through the rear windscreen of the truck, you can clearly see the highway and all the cars on it behind them. Amelia turns the steering wheel sharply to the left, and you hear the screeching rubber-tyres-on-tarmac noise as if she really had swerved left, but the scene of the highway behind them seen through the rear screen does not alter at all - as if she was just going in a straight line all the way.
Continuity mistake: When Amelia jumps in the water to save the the little girl there is tape on her mouth. A moment later, the tape is not visible.
Continuity mistake: Nearly at the end of the film Amelia falls into the sea to get the old man and the girl out of there. Her clothes of course get wet, but later when she discovers the taxi of the murderer her clothes are dry.
Continuity mistake: When Rhyme is playing chess on his computer, the piece movements don't match the voice commands he gives.
Continuity mistake: Near the end when Lincoln is being attacked in bed, Richard (Marcus) breaks Lincoln's left index finger. In the final holiday celebration scene, Lincoln's right finger is bandaged and his left is fine.
Chosen answer: The killer used to be a forensic scientist for law enforcement (where or when is never stated). Rhymes testified in court that evidence had been falsified, leading to wrongful prosecutions, the killer was sent to prison for this, where "every day I was brutalised". The killer blamed Rhymes for this, so set out to prove he was better by giving him a series of clues that he (in theory) couldn't solve. It should also be pointed out that Rhymes never met the killer or knew what he looked like.