During the terrorist attack, an American soldier starts firing a 50 cal machine gun from the APC at the main gate location. There's little doubt that the 3 terrorist trucks and occupants would have been obliterated by the lethal power of this gun, yet they all drive away unscathed.
When Jack gets out of the helicopter, some seat belts or straps fall out the opening, but when the shot immediately changes to a wider shot, the straps are gone.
When the helicopter lands and the crew chief opens the cabin door, the seat belt falls out. A moment later Jack Ryan steps out and the seat belt is not in sight.
When the Arab wife goes into her own home with the tea, a mourning dove sings. Those birds are not found outside North America.
The Coast Guardsman at the party verbally identifies himself as "Petty Officer Second Class Dillard." However, several name tags on his uniform show the name "Harrity."
When Teresa brings coffee for Jack, it's obvious from the way she waves the cup in her hand, and the lax angle with which she holds the tray with her own cup of coffee, that the cups are empty. Also, when she sets Jack's cup on his desk, you can hear a sound that could only be made by reverberations through an empty cup.
When Greer is checking Jacks military record at 31:09, a few obvious spelling mistakes can be seen. "..God conduct..", "..Certificat...", "..Riffle.."
When Jack watches "Jeopardy" at home, the questions are from two different shows (one that aired in October 2016, the other from November 2016).
The metronome was ticking when Jack woke up and checked the clock at 4:47AM. Unless he had wound up the metronome at around 4:40AM or later, it wouldn't have kept ticking back-and forth for more than a few minutes. All traditional metronomes - as the one shown in the movie - require manual operation.
Jack is picked up by Coast Guard helicopter in Maryland and dropped off at an Air Force base to board a CIA plane. However, the B-52s in the background at the base with the tail code "LA" indicate that the scene was shot at Barksdale AFB, LA.