Visible crew/equipment: When the boxing scene starts, as the camera pans past the punchbag, the shadow of the camera is clearly cast on it. Then as the camera continues to pan past the punchbag, you can see the sides of two crewmembers come into view (who are following the path of the camera.) They are both wearing a jumper and jeans.
Continuity mistake: When Rennie is being pushed overboard, notice the guys sitting in the background wearing a blue shirt. When it cuts from below the ship, as we see Rennie falling, the guy is gone. Also when Miss Van Deusen goes for the life ring, we see from below the ship that the guy is gone. But when it cuts he is there again.
Continuity mistake: The black sludge on the girl's white pants when she's in the sewer at the end is constantly changing. It sometimes changes position or isn't there at all in later shots. The best example is when she lures Jason away from the guy that just got knocked out and runs into the dead end. She slides down the wall next to the toxic chemical container and the back and sides of her pants are completely covered in the black sludge, when she runs away, her pants are totally clean.
Other mistake: Jason seems to be able to teleport in this film. Most notably towards the end when Mr. McCulloch is running from him down an ally, Jason is behind him, then in a matter of seconds he's on the top floor of a building, without ever entering it, in time to throw McCulloch out the window.
Plot hole: Jason all of a sudden can drive a boat and out of nowhere, seems to know about a cruise ship filled with teenagers ready for him to kill. Yeah, makes sense to me. Especially since there is land with buildings right where Jim and Suzie drop anchor on their boat. Jason gives up killing people in those buildings to drive to a cruise ship that he cannot possibly know about? Also the fact that the survivors get to New York and minutes later Jason just happens to pop out of the water? Are we led to believe that he not only learned how to swim to New York but he managed to not kill everyone while they were in the life raft?
Factual error: When Rennie and Sean are on the ladder and the toxic waste is flooding through "destroying" Jason, they are completely unscathed. There is no way there would be no splash back burning them, plus the fumes from the toxic waste which they are subjected to would have done them serious bodily harm.
Revealing mistake: During the part where J.J. goes down to the boiler room to play her guitar, Jason sneaks up behind her. She screams and runs down more stairs, and then right before Jason kills her, as he lifts the guitar to hit her, in the lower right hand of the screen you can see the blood coming out of the guitar before it hits her.
Continuity mistake: Rennie's visions of Jason as a boy change their appearance constantly throughout the film. At some points he is bald and deformed, much like how he was in the original film. At other times he appears as a normal, non-deformed boy with a full head of brown hair. At some moments he even appears as a mix of both (with a deformed face, but a full head of hair). This inconsistency is never explained or even acknowledged.