(at around 1h 15 mins) When Frank fights Tanaka's daughter, after he pins her to the wall, she takes both her earrings off and scratches him. In the next shot her earrings are back on and then they're gone again.
(at around 27 mins) Punisher's sidekick misquotes Macbeth when entering the sewers. He says "Bubble, bubble, toil and trouble" when any thespian will know the correct line from MacBeth begins "Double, double...".
(at around 1h 10 mins) After the lights go off, some goons shoot at where two characters are standing, only to find them gone when the emergency lights come on. Not a single bullet hole is visible in the Japanese paper screen they were standing before, however.
(at around 1h 11 mins) While Frank Castle is fighting a Japanese Swordsman, a holstered gun on Castle's back disappears. Moments later, it re-appears in the holster. The weapon wasn't touched by anybody.
When the Punisher is arrested, a newsreader says that he has been charged with 125 murders, even though that was the amount of murders he had committed before the movie takes place, and he had killed a lot more people since then.
(at around 47 mins) When detectives Berkowitz and Leary go down into the sewers to search for The Punisher's lair, Berkowitz explains how he met Frank Castle. As they round a corner a film crew member's leg is visible in the corner of the shot, and they quickly move their leg out of the frame.
(at around 1h 10 mins) After the Japanese henchmen are shot at through the paper screen, the very last extra to be shot dies unconvincingly. He slowly drops to his knees, leans forward, and carefully places his weapon down.