Fusco handcuffs the Samaritan agent Jeff Blackwell's hands from behind but later on when he reaches out to his knife to stab Fusco, his hands are tied from the front which makes his attack and escape possible.
When Harold is having the conversation with Samaritan in Times Square, the sky is pitch dark. In the next scene when he is on the rooftop it's bright daylight. That transition, plus the time to walk from the bank to the office building and get up on the roof is supposed to take place in less than 18 minutes from when Finch and Reese were in the vault.
While Finch is in the Federal Reserve building trying to destroy the only remaining copy of Samaritan inside an air-gapped computer, Samaritan escapes once again, sending a copy of itself to a Midtown building with an antenna to be sent to a Russian satellite. It wouldn't be possible to do since it was supposedly inside an air-gapped computer which would mean it would have no access to the outside world and completely unconnected from all networks.
Finch says that in order to preserve itself, Samaritan sent a copy of itself to an air-gapped computer in a vault inside Federal Reserve's building. If the computer is truly air-gapped, that means Samaritan couldn't reach it in the first place and couldn't send a copy of itself. If the computer isn't truly air-gapped, the Finch's virus would have reached it and destroyed Samaritan's copy there.
Reese didn't know how to program the Machine but in this episode he programs it to direct the missile attack towards the satellite antenna.
Earlier they explained that Samaritan had preplanned a missile launch upon the uplink building. Reese wasn't programming the missile strike; he was uploading the virus.
Earlier they explained that Samaritan had preplanned a missile launch upon the uplink building. Reese wasn't programming the missile strike; he was uploading the virus.
Reese was locked in Federal Reserve's underground vault by Finch. In the next scene, he appears to be out already with no explanation as to how he got out. Even if he was able to get out of the vault somehow (impossible), he would have been arrested or shot on spot by the armed forces in and around the building since the building was in high-alert mode.
When bad guys are about to execute Reese and Fusco, some sniper mysteriously shoots all the executors. No explanation who that sniper is and why and how this sniper was able to locate and shoot all those executioners.
An EMT is performing chest compressions on a man lying in the street while the man's legs are bent and causing his body to twist. One of the EMTs would have straightened his legs so the first aid would be more effective. If the medical personnel were concerned about a spinal injury, one would have put a cervical collar on his neck.