In the desert, Marty brings Billy the two guns after Hans leaves. Billy takes both guns in his right hand when he starts to stand. When the camera angle changes, though, he twirls just one gun in his right hand.
When Billy begins his assault during the final shootout, the Beretta in his right hand runs out of ammo at one point and the slide locks back. The immediate next shot shows the slide back in the released position.
At the final showdown, the Jack of Diamonds that is facing the camera in Bonnie's collar moves from the right front to the back left of the dog's neck. This cannot be explained away by the collar slipping around its neck, since the face of the card would be facing away from the camera and into its neck if it did slide around there.
At one point when Hans and Charlie are sitting across from each other in the hospital waiting room, Charlie asks "are you hurt?" Charlie is sitting upright when he says this, however the very next shot from over his shoulder shows him leaning forward.
The masked killer on the bridge throws down two playing cards. In the first shot, those playing cards have a pattern on their back. In the counter shot (showing how the cards land) the cards have matching front and back - both sides show the jack of diamonds. This was probably done to not have to go through repeat takes until the cards landed with the jacks facing upwards.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
Hans' story he left on his recording device about the Vietnamese priest is factually impossible. The priest/monk could not have lost his family in the My Lai Massacre (which occurred in 1968) and then become the first Buddhist monk to self-immolate in Vietnam, which occurred in 1963. However, the monk's story was meant to be a dream sequence in which the monk saw himself as a vengeful Vietcong warrior, while he was in fact a pacifist monk.
When Marty drives away from the final shoot out and stops off when he sees Hans's body in the road, you can see Hans breathing - his stomach clearly moves up and down - even though he is supposed to be dead.
In the close-up shot of Billy shooting Angela, Charlie's girlfriend, in the stomach, we see the squib on her body explode before the trigger is fully pulled. Also, no gas is expelled from the gun, revealing that not even a blank was fired.