The woman says that Andrew Bornstein is 23. A few minutes later, when checking on Aleksandr Chercheront, they find out that he's alleged to be dead at 9 years old in 2004. Considering that the action takes place in 2013, that would make him 19 at the most.
(at around 1h) While Cherevin is escorting Carthy to the restroom, one of the CIA agents picks Cherevin's pocket, using his left hand to steal Cherevin's wallet. Simultaneously the agent is holding his phone in his right hand. In the next shot, the stolen wallet is in the agent's right hand.
While Jack Ryan breaks into Lemkov's office, the rim design of Dimitri Lemkov's car changes. When Lemkov leaves, the wheels are light-gray; then, when he notices that someone broke into his office and he turns his car around, the wheels are black and clearly bigger.
Jack Ryan is shown attending a movie at Film Forum, a real cinema in Manhattan; however, the inside of the theater Ryan is in has stadium seating. None of Film Forum's three auditoriums have this kind of configuration.
After returning to America from Russia, presumably at Andrews Air Force Base, Jack boards a helicopter for the first time since his accident. In a sequence of quick shots, the helicopter lifts off with landing gear down, then up, then down again, and finally up.
At the beginning of the film Jack Ryan is in a park of what appears to be a rural university campus. He then enters the Old Building of the London School of Economics. The London School of Economics is in the middle of central London.
When Ryan is doing rehab, he is using the crutch on the presumably weak side (right leg) of his body. Modern rehab teaches you to use the crutch on the strong side. The idea is to use the crutch to shift your base of support away from your injured side. A modern medical student should know this.
During worship in a Russian Orthodox Church, the characters are seated as they listen to a reading. In Divine Worship in a Russian Orthodox Church, the congregation would be standing, not sitting, throughout the entirety of worship.
During the opening scene, Jack lies upon a bench, his head resting upon a trade paperback textbook entitled, "Further Mathematics for Economic Analysis." The setting of the shot is the London School of Economics, September 11th, 2001. The first edition of that said text wasn't published until August 14, 2005.
In Michigan, at the Russian Orthodox church, the cross displayed is the Latin cross common to many forms of Christianity, but not the Suppedaneum cross (which has three bars - one above the arm bar where inscription was placed, and a slanting foot barcross) used by the Russian Orthodox.
When the voice over of Jack Ryan being sworn into the U.S. Marine Corps is heard, the oath is the oath of enlistment "...I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me..." rather than the oath of office appropriate for a lieutenant, "...I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God."
At the trading company Jack Ryan works for there is a scene of him speaking with a superior about the possibility of Russia ripping off the firm. The year is 2012 and Jack's superior states that Russia is very lucrative for the company and Russia is the "Wild West" for traders as insider trading is legal; however, in January 2011 Russia passed a law which made insider trading illegal. There is no way a trading firm would not know this, especially a firm with large and lucrative Russian accounts.
When Jack is in the field hospital after the helicopter crash, the doctor is saying he has a spinal fracture and needs a foraminotomy or possible spondylolisthesis. Foraminotomy is used to fix a pinched nerve in the spine, not for a fracture. Spondylolisthesis is not a medical procedure. It's a condition where one vertebra slips over another.
Although the film revolves around Ryan and without him there's no story, as operatives of the CIA, he and Harper are not allowed to take action on American soil; they would be prohibited from taking part in the operation to stop the terrorist attack.
Aleksandr has spent a lot of time and effort turning his van into a convincing replica of an NYPD ESU van, complete with bull bars, steel rigging on the roof, and working emergency lights and sirens. This poses quite a few plot holes: (1) It is implied he has done this all by himself in a matter of hours. This would have required a lot of heavy lifting and electrical work; even for a company doing that sort of conversion, this would require several hours if not days. (2) It would be quite conspicuous, especially to law enforcement agencies, to see an NYPD van cruising around in Pennsylvania, way outside of NYC. (3) Obtaining such equipment as emergency lightning, sirens or NYPD decals would usually require clearance from the buyer proving that he works for a law enforcement agency or another authorized agent. The combined purchases of all the equipment used to disguise the van would at least have raised a few flags for the CIA analysts. (4) It is implied that Aleksandr's plan was to blend in with the emergency units evacuating Wall Street. That means he would have anticipated early on that the authorities would be on to all the details of his plan; however, this whole plan proves to be irrelevant later on as he conspicuously crashes through a construction site, away from all the commotion, to reach the tunnel. It would have been much easier and much less costly and time-consuming to simply disguise the van as a rental or delivery van.
In the beginning of the movie, the attacks on New York on 11 September 2001 ("9/11") are shown on TV. The TV is shown in a reflection, but the image of the two towers on fire immediately following the second airline crash, is shown the right way.