Factual error: As Reddington sets up the blood transfer between himself and Ressler he inserts the intravenous line in Ressler's arm first and then in his own arm. This is a big NO NO! This way the remaining air inside the line gets into the recipient's body and could very well kill him. Judging the expert way he handles the set up he should know to first insert the IV in his own arm, let the line fill with blood and then insert the IV in Ressler's arm.
Plot hole: At the end of this episode Red takes off his shirt revealing his burned back, which leaves us to think that he might be Elizabeth's dad. However, this particular mark should have been noticed and written down in Red's prisoner file when he was taken into custody the first time (Episode 1). In that case Elizabeth would already know that Red is burned and could have asked some questions about it.
Factual error: Tom Keene watches an arms deal. The supposedly German plates of the BMW read "DD17-36F9." This, however, is not a possible combination in Germany, as there would not be numbers in the first half, nor a letter after a number in the second part. [exceptions from the first being the most important officials' cars like the federal president's, but even then the latter applies.]. Furthermore, no more than 4 numbers can be used, except for in police and military vehicles (which also never have a letter after a number, and start "Y" for military, or "DD-Q" for Dresden police). "DD-F1736" would have been a correct plate for the town of Dresden, for example.
Continuity mistake: Agent Keen breaks the train window and dives through the broken glass and cuts her face in two places as she pursues the young man. Her two cuts alternate throughout the following scenes on the train from dripping blood to barely scratches. That evening at home with her husband her face is practically clear and at Reddington's home later that evening her skin is perfect.
Continuity mistake: The BMW 5 Series equipped with the dirty bomb you see in the beginning of the show is one of the 'F10' type. The car that actually explodes is another car. Possibly an elder 5 Series 'E34', but not an 'F10'. Later in the episode you see the F10 again, but when the FBI agent starts the BMW, the interior of an 'E60' BMW 5 Series is shown.
Other mistake: After arresting the Reddington impostor, Ressler states that while hunting Red they had only one photo with a "passing resemblance to the man we've been working with." In S1E1 you can however see a high quality picture of Red on the front desk screen while he is arrested.
Factual error: Aram tells Elizabeth he downloaded "the fourth series of Doctor Who" and "Tom Baker is amazing" (indicating Baker is in series 4). Aside from unusual series/season word choice (Brits more often use the word "series" whereas Americans use "season"), Baker was the 4th Doctor and did not appear until season 10 of the original run.
Revealing mistake: In the shot of the assassins fleeing the scene of the bullet-ridden Range Rover in Shanghai, China, people are casually crossing the busy street in front of and behind the car. Nobody is looking at what just happened. Computer generated graphics were used to place the car and assassins motorcycles in the shot.
Factual error: Early in the episode, a detective knocks on the door and identifies himself as being from the Metropolitan DC Police Dept., and displays his badge. Apparently the prop department gave the actor the wrong badge, because the one he flashes is from the NYPD, not the DC Police.
Revealing mistake: When turning the guy with C4 around his neck, the 4 person safe box window shakes briefly. If this was a bomb proof safe box, the glass would be at least 1.5"+ in thickness and would not shake simply from some walking. That box would be shrapnel to a C4 bomb inside.
Character mistake: After Elizabeth and Alexander Kirk crash-land into the Gulf of Mexico (technically, the Straits of Florida), Lizzie gets on the radio to report mayday, along with their coordinates. She incorrectly states their position with the following statement: "Mayday, mayday. Plane down off the coast of Havana. 23 degrees, 52 minutes north, 82 degrees, 49 minutes south. Mayday, mayday, mayday." Those coordinates specify two different latitudes (one above the equator, and one below), but no longitude! Luckily, she DID say they were off the coast of Havana, so the Coast Guard would be able to deduce the correct coordinates of 23' 52" north, 82' 49" west (not south!).