When Leo calls Dean to his office to hear the recording of Simon's call it is played back out of order. The original was Leo asking, "Who is this?" and Simon responds, "You are a stranger." Then Leo asks where he got the number from and Simon gives the puzzle number and Leo asks, "What did you say?" then you hear Simon's mother telling him to hang up the phone. The recording is played back with Leo asking "What did you say?" Then Simon's mother telling him to hang up the phone.
When Art gets out of the ambulance and climbs the fence with Simon he goes over first and then lifts Simon over. Art holds Simon tightly as he crawls on the ground between the fence and a train track. Art pauses and peers down the highway having never released Simon. Then, one second later, Simon is a hundred yards down the track, behind Art, walking headlong into an oncoming train. It's impossible in the transpired time for Simon to have covered the distance at his meandering pace.
When Simon calls the puzzle line the second time, Art takes the phone and speaks to Dean but does not say his name, only that he is FBI. When Art meets Dean the following day Dean knows Art's name is Agent Jeffries.
In the final part, when Stacey and Simon look to the huge building they about to enter outside it's still day light; after a few minutes, when they are on the roof of the building, outside looks like midnight.
As Simon removed the cap from the marker before starting a puzzle, he set the cap down. The next few shots, the cap was attached to the marker as he was working on that puzzle. When he finished the puzzle, the cap is back on the table and he picked it up from the table.
When Art Jeffries (Bruce Willis) is driving the stolen ambulance on the freeway, the assassin takes two shots at Bruce and Simon using a silenced pistol. The second shot shatters the ambulance windshield; this is not possible since all windshields are laminated glass. in reality, there would only be a small hole in the windshield, maybe the windshield would be cracked, but definitely not shattered.
When Art is driving the ambulance, we see it from the front, with the word "Ambulance" clearly readable. However, the word is always printed in reverse on the front of an ambulance, so that it can be read by drivers looking in their rear-view mirror. The film has not been flipped, because it's clear that Art is sitting in the ordinary driver's seat.
The "$1,500 gun" that Jeffries identifies as the weapon used to kill Simon's mom and dad is a H&K P7. More suspicious than the fact that the gun is very rare and expensive would have been the fact that the barrel would have been an extended threaded barrel to attach a suppressor. These are only purchased when a person intends to add a silencer to the gun.
Kudrow insists repeatedly that the autistic boy's breaking the code puts agents in the field in danger. However, early in the movie, the two computer nerds establish the code is not yet in use. They placed it in the puzzle magazine as part of testing before implementation.