When Hannah woke up her shirt was thoroughly bloodstained. When she walked downstairs her shirt (the same one she was wearing) had no blood on it at all.
It is impossible that security wouldn't notice a barrel poking out of the only open window right across from the Capitol. Counter snipers would take the shot.
When Agent Wells attempts to prevent the sniper from taking a shot, it is impossible for the handgun she is using to fire a bullet the distance needed to reach the shooter.
Seth states that Thomas Jefferson was inaugurated in 1800. While Jefferson was elected President in 1800, his inauguration took place on March 4, 1801.
There are 2 tall buildings seen from the Capitol (where the shooter is) that are not actually there and never would be as there are building height requirements limitations so that the sight of the Capitol dome is not blocked from view.
When agent Wells arrives at the former chief of staff Langdon's hideout she parks her car directly in front of the garage. When Langdon escapes in the car parked in the garage, her car is gone.
There is no such building that close to the Capitol. Also, most office windows do not open out (if they did an item dropped or falling from a higher window would break it).