When Suleiman gives Hanin (his wife) a jeweled necklace as a gift, after he puts the necklace around her neck, it is shown right (or front) side up, but seconds later when the camera is showing only her, the necklace is shown wrong (or back) side up.
The MRI that Ryan's doctor is examining/interpreting is actually from a 55 year old female. The screws seen (which are not properly placed) are fusing the L3 and L4 vertebrae, not L4 and L5 as stated. The doctor would also not be looking at an image with so many scratches or marks on it.
Between minutes 39 and 40, when Greer, Ryan and French Police SWAT team enter the building in Saint-Denis near Paris, the kid playing on ground floor sends a warning text message to Ali. The message reads '5-0' which is the way an American would warn someone. A French (speaking) kid would have sent '22'. Explanation and history can be found in French on Wikipedia by searching '22, v'là les flics !'.
Despite the effort put forth to convince us that Jack is an avid fan of baseball, he refers to SunTrust Park as SunTrust Stadium. A fan that can instantly quote current player stats, as he does in a quick conversation about which pitcher to start in a fantasy league, would not make that mistake.
When Ryan is picked up by a USCG HH-60 Jayhawk, they are somewhere near Washington DC, and then suddenly they are surrounded at a Air Force Base with B-52's bearing the Tail Code "LA". 'LA' is the code for Barksdale AFB in Louisiana, the HH-60 Jayhawk does not have the fuel range to fly from Maryland/Virginia to Louisiana.
Jack Ryan meets with Singer in Singer's office. Singer relates that he was a rower at Yale undergraduate. Ryan is sitting on Singer's couch under a rendering of a college campus, which supposedly is Yale. But the rendering is an old print of the Colgate University campus, not Yale.
Around minute 7:30 the two brothers meet in a port in the 'Gulf of Aden, Yemen', which is vague enough. When the camera pans out, Moroccan flags can clearly be seen flying from flagpoles.