When Gregory Peck is calling a telephone number, the "Not in Service" recording starts before he is finished dialing.
When David Stillwell finally knocks down Willard for good, Willard's gun lies near his armpit, but when Ted Caselle picks up the gun, it's on the other side of Willard's arm near his shoulder.
When Willard fires, the bullet ricochets and almost hits Josephson at a sharp angle. That's not how ricochets work. In a real ricochet, after the bullet hits the hard surface, the bullet then continues on at a shallow angle, not a sharp angle similar to the angle of approach. Hence, if a bullet strikes a surface at a 45-degree angle, the bullet then continues at a shallower angle, like a 20-30% angle.
In the office building basement, Willard fires three shots at Caselle with his semi-automatic pistol. The gun's slide locks open, indicating an empty magazine, but Willard immediately fires a fourth shot, without time to reload first. At that point, the gun had already been empty and unable to fire the fourth shot.
When Caselle ducks behind a wall to be shielded from Willard, there are already bullet marks on the wall, probably from previous takes.
When David Stillwell is giving his information to Lt. Franken, Franken only pretends to type. After David gives his name, Franken doesn't type out enough letters. After he gives his address, including apartment 7G, Franken's fingers never hit the number keys, and his last entries simply repeat the same two keys rat-a-tat-tat.
After leaving Joe Turtle's apartment and hearing the police enter the ground floor, David and Shela supposedly go up one floor. From the pattern of staining on the underside of the stairs, one can tell it is the same hallway set, just redressed to appear as another floor.