Wyatt's wedding ring appears and disappears. Before they go to find JFK, he isn't wearing one -- but when they're at the hospital, he is.
After Flynn opens a beer for Lucy, he places the bottle opener and bottle cap on the coffee table. As the camera pans over his shoulder, the opener is there, but the bottle cap is gone.
Wyatt hides behind the corner of an interior wall at the party when shots are fired at him. The bullets penetrate the facing side but he is unharmed. In reality, the drywall would not stop the bullets and he would have been injured.
When Jack Kennedy reads about his elder brother's death, it is referred to as happening during a mission over France. It actually happened near the village of Blythburgh in Suffolk, England.
The phone number Gramercy 5934 is missing a number and would be incorrect. In this period, exchanges were identified by a name and the first two letters were used and then the last five. The exchange should be GRamercy (or 47), the missing number, and then the 5934.