Revealing mistake: When the man is pushed out of the helicopter and hung by a noose around his neck, in the brief close-up shot you can see the prop noose around his neck is very loose and partially conceals the real rope that suspends the victim.
Revealing mistake: As soon as Tony shoots Hector out on the street, the shot changes angles to see Hector's body fall face down. It may be a stunt-double because this person's hair is completely different from the actor playing Hector. Before Hector is shot, his hair is completely combed. As his body is falling, his hair is suddenly completely uncombed (To me it seems the double's head is bald on top and with a tiny pony-tail, but that's probably just me). After he falls his hair seems back to being combed-over.
Revealing mistake: At the end of the infamous chainsaw scene Tony takes an automatic pistol away from one of the Colombians after a struggle in the shower. Tony pushes the Columbian away, extends the pistol and fires a round. You see the gun's hammer drop and the muzzle flashes, but the slide does not cycle, a clear sign that blanks were being used.