Continuity mistake: Alexander still had the mark/cut on his forehead, running vertically to the outer edge of his right eyebrow, when he found the "Mars" candy bar, but it was gone less than 30 seconds later (after he found the gun). The angle as well as its appearance (wider, longer, straighter, and more pronounced) of the mark/cut on his right cheek also changed. (00:02:20 - 00:03:26)
Continuity mistake: When two officers go to inform Ronald Whitlock (Bruce Willis) about his sons, Ronald shoots his pistol at the Black officer and hits him near his inner right eyebrow. (A large black spot can be seen between his eyebrows.) When the camera shows the dead officer, the black mark is gone and the bullet hole is on his forehead centered about 2" above his left eye. (00:06:40)
Continuity mistake: During the musical montage when Neo sees again the birds fly in the same pattern, there's a bit when "Tiffany" gets her order from the counter and exits the coffee shop. Neo is eating from his poke bowl, chopsticks in his left hand. His right hand is flat on the table, but in the next shot we see him through the window, and his right hand is turned 90°. (00:26:25)