As John and Leon are on the first floor of the parking garage, Leon is wearing handcuffs. While climbing the stairwell with John, the cuffs are gone, only to reappear once Leon reaches his car.
When Reese figures out how to decipher the number the machine gave him, he places the books in a different order than the machine told him. Based on the order the machine gave Reese the words, the number would be 006013062, but Reese put the books to read in the order 013006062, which is the number he gives Fusco to put a name to the number for him, thus he's looking into the wrong POI from the one the machine gave him.
The facial recognition frame on Caroline (aka Root) in the opening sequence is white instead of yellow as it was in the season 1 finale.
When Reese and Tao are on the corner and Reese is giving the machine the ultimatum to get help finding Harold the phone rings and gives the code " Ayacucho-Golf-Papa/Deterministic-Hotel-Sierra/Camera-Kiosk-Kilo". Yet when Reese is looking up the information on the article about a missing girl the top book shown in the stack which should say Camera-KK instead says Camera-SK.
While Harold is crossing the street outside a casino in a flashback dated September 2003, a Chevrolet HHR is visible twice. The HHR made its debut in 2006.