(around 21 min) There is a title card that displays the date as Nov. 18th, 1963 (4 days before the assassination). The very next scene shows Lee Harvey Oswald sitting on a park bench reading a newspaper that clearly has a headline that says:
"Kennedy arrives tomorrow, November 21st"
If the next day was Nov. 21st then that means it was Nov. 20th when he read the newspaper, not Nov. 18th like the show had previously stated.
The high school yearbook picture of Sadie and Jake dancing the Lindy Hop is captioned "Miss Dunhill and Mr. Epping." Jake was known at the school as "Mr. Amberson."
When Oswald beaks the bead chain holding the pen to the base on the desk, beads roll all over the desk. A bead chain is not a string of beads. It is a type of chain made of hollow balls linked to each other by small, pin-like sections of metal. When a bead chain is broken, it's just broken and all the pieces are still attached to each other except at the break.
At the doctor's office in the clinic "for people who can't pay", right after the doctor says Bill was on electroshock therapy, a prolonged electrical arching noise and screaming is heard. Electroshock lasts a few milliseconds and patients lose consciousness at the beginning of the impulse. Despite its bad publicity and the damage it may cause to the brain if misused, electroshock therapy is not physically painful.
When Lee leaves his bedroom for the last time on the morning of the assassination, he carries the "supposed" rifle wrapped in paper that he told his friend Buell were "curtain rods". The real Buell Frazier has stated that the "package" was short enough to stick under his armpit and rest in his hand, when the package is clearly 4 feet long which precludes it from being able to do that.
On the morning of the 22nd of November, Buell Frazier drives Oswald to the School Book Depository and parks in the rear parking lot of the School Book building. In episode 7 it shows both men approaching the Depository and talking about Kennedy's arrival in town. In reality after parking in the rear parking lot, Oswald walked ahead of Frazier and entered the building alone leaving Frazier behind doing some business in his vehicle.
When Jake awakens in the hospital with visions of modern-day, a man is pushed down the hallway in a wheelchair speaking on an iPod touch (5th generation) as though it were a phone. It is possible the man was using the wifi feature to make a phone call. Several apps have been built which allow this.
When Lee Harvey Oswald is walking to the Texas School Book Depository, the plaque that commemorates the assassination is visible just above the cornerstone of the building.