When Mama One is taken from the helicopter into a car, there are several cars and a truck following. In the next shot from within the car there are no cars at all to be seen through the back window.
When Ireland and Bronson's characters are being chased by Bracken in the Pickup truck they are shown to be on a two lane highway. In the middle of the chase there is about one second when you see they are being filmed on a one-lane dirt road before they actually turn onto the dirt road.
In the long shot of Killy on the bike right after the freight train's whistle starts to blow, you can see a very great distance behind Killy down the empty track, with no pursuing hitman's pickup truck visible, even though it is always shown following fairly close behind Jay and Lara in previous and subsequent shots.
The airplane call sign used by Lara does not match the registration number on the outside of the plane.
The college Killian tells Lara he attended does not match the diploma on his office wall.
Far too many shots are shown to be fired in all of the pursuit-by-automatic-weapon-toting-mercs/agents sequences; even high-capacity box-magazines only hold a maximum of maybe 30 to 50 rounds, yet many dozens of shots are always seen and heard to be discharged without the mercs' reloading another clip.
The plane shown as being used by the vice president in California is SAM 26000, which was the primary plane for the president's use a/k/a Air Force One. That plane should have been on the East Coast where the president was, not in California with the vice president.
The Inaugural Procession down Pennsylvania Avenue is depicted as happening before the Inauguration. It actually happens after the swearing in.
Killion clearly greets the Chief of Staff, Hector Bunsen, as 'Senator" and addresses him as "Senator" later in their conversation. The Senator acknowledges he represents Hawaii and is referred to several times as "Senator". US Senators do not serve as the President's Chief of Staff, not even after they've retired from the Senate.
The First Lady notes that fifteen thousand men were killed during Pickett's Charge, but this is not true. There may have been up to fifteen thousand Confederates that took part on this Friday the third of July, 1863, under Major General George Pickett, but records show that no more than about 2500 were killed in this charge alone, which itself was one of the final acts of the three-day long Battle of Gettysburg.
Presidential inaugurations are in January but footage of the motorcade shows trees in full summer bloom and people in summer clothing.
Faded paint on the top rear exterior wall of Killian's hotel in Washington D.C. reads "Mar Vista Hotel" which is in Santa Monica (where scene actually filmed).
Obvious stunt-double (younger man, different face, darker/differently-styled hair and mustache, etc.) when Killy jumps off the bike to avoid a rocket round.
The timer casually slapped on the plastique under Cappy's boat is visibly beginning to fall off just before the shot ends.
The jetski-riding hitman sends the C-4-laden motorboat throttling forward towards the shore at full speed, yet the boat is clearly motionless (small wavelets just lapping placidly around the motor's outdrive, rather than the water's streaming back from it in a long foamy wake) in the shot of the outboard's catching fire after being hit by a bullet.
An assassin working on the First Lady's father's boat in a dry dock attaches a time bomb to the hull. Back in the water it's taken to a fueling station where there's an explosion but it's fuel station that goes up in flames and not the boat.
On board the train Killian asks Lara, "how did you get your name? Did your mother read Doctor Zhivago or something?" Assuming this fictional story is set in the present (1987), Jill Ireland --- though young-looking --- was born in 1936. Doctor Zhivago was first published in 1957, 21 years after "Lara" was born; at the time of Lara's birth, her father could not have been familiar with the book yet.
The motorcade traveling easterly from the White House to the Capitol passes a sign facing east and pointing to the Federal Triangle on the left and the National Gallery on the right. However, they are supposedly on Pennsylvania Avenue, which is the northern border of the Federal Triangle, and the National Gallery is south of the Federal Triangle, so both arrows should be pointing to the left (south).
Lara boasts to Killian that she's vacationing in secret by carrying $25,000 in travelers checks under her maiden name. Lara's family is rich and famous. She could and should have gotten totally untraceable cash because the maiden name of the First Lady is not exactly a secret.
Fitzroy says John Wayne Airport is in Newport Beach. It's actually in Santa Ana.