When the KGB agents chase Javorski, the scene cuts between day and night repeatedly.
The boys that wander off, while the parents fix a flat tire, are alternately named by the Mother Randy ,Art. The father Mike and Randy and to each other Randy and Art.
The Beast wears a suit jacket during the shootout. The jacket disappears a few seconds later.
At 39:24, Mrs Ratcliffe is standing in the middle of the dirt road with tire tracks present She stops. At 39:36 she is seen on the side of the road and walking to the middle of the dirt road with the same tire tracks only now their car is mysteriously parked in the middle of the road.
During opening car chase, the scenery repeatedly changes from desert to forest to mountains and back.
The beast somehow enters, unnoticed, the small 2-door car to strangle the female passenger from behind, and then exits the car. This is not possible, especially for someone as large as the beast.
Part of the plot involves a secret Soviet moon landing that is being kept under wraps. Given how eager the Soviet Union was to prove that Communism was superior to Capitalism in every way (technology, economy, industry, etc), if they had really made it to the moon ahead of the Americans, they would've sooner embraced capitalism, McCarthyism, and McDonalds than hide that fact from the entire world.
When the police officer on plane opens the window and starts shooting, neither the strap around his gun nor his hair blow in the wind that would be created by a plane moving at such a high speed.
Before the opening credits a sequence featuring a naked woman after a bath or shower is seen drying herself off and wrapping a towel around herself. While sitting on her bed ,finishing drying herself, she does nothing as "The Beast" calmly walks up and strangles her.
The Radcliffes get a flat tire and pull over on a desolate desert highway. As the Dad changes the flat tire, the shadow of the film crew vehicle is right behind him, along the side of the road.
When the aerial rifleman takes his first shots, the rifle scope cover is still on the rifle.
When Joseph the "Beast" strangles the 3 people in the broken down car at 9:40, none of them struggle but are completely still and just succumb. The girls hands are clearly visible yet she makes no effort to struggle and just dies quietly.