(at around 29 mins) We are shown Jason's perspective as he is walking down a hallway towards the sauna. When Jason enters the sauna, we can clearly see there is no hallway across from the door which makes the previous scenes impossible.
In the previous movies, Crystal Lake was a lake surrounded by land; in this film, there is suddenly space for a small yacht and a channel that feeds into the open ocean.
(at around 37 mins) When Tamara comes out of the shower, she's completely dry, hair and all.
(at around 56 mins) As the engine room floods, Rennie and Sean get soaked, but when they run upstairs, their clothes are completely dry.
(at around 1h 14 mins) When the cop gets pulled from his car by Jason, they are in an alley right next to the car. But in the next shot, Jason is standing a good 20 feet away right in front of the car.
(at around 1h 14 mins) In the NYC police car, there is no screen separating the front and back seats.
If the toxic waste that floods the sewers every midnight is strong enough to disintegrate Jason, the area would be sealed and no one would be working down there. In addition, Rennie and Sean would likely be overcome by fumes hanging just inches above the surface while Jason dies below them.
(at around 1h 29 mins) Sewer tunnel entrances in Manhattan are barricaded.
When the brake is pulled on the moving subway, the momentum would have thrown Jason forward toward the protagonists, not backwards.
(at around 7 mins) Throughout the film, Jason's skin is grey, slimy and decayed, except for the pinky finger on his left hand, which is completely normal, protruding through his torn glove. This is especially noticeable in the extreme close up of Jason grabbing the railing of Jim's boat near the beginning.
(at around 1h 22 mins) When Shaun and Rennie run through the two glass doors leading down into the New York subway system, you can see Jason's shadow on the wall as he stands off camera and waits for his cue to walk on screen and kick his way through the glass doors.
Obvious stunt double for Rennie when Sean leaps into the water to save her.
(at around 30 mins) When Tamara pushes Rennie overboard, the ship is obviously not moving or it would have left her far behind. Also, the water is calm with no waves from the boat.
(at around 44 mins) When Julius says, "school is out, McCulloch" and several students leave, you can see red and green building lights in the left window.
Charles says that Tamara had better have her Biology final done. If they're on a graduation cruise ship, the school year must already be over and thus finals would have already happened long before the cruise would have taken place.
During the rain storm the ship appears to rock quite significantly from side to side (a camera effect). The rocking has no effect on characters moving around the ship or various props which all behave as if the ship is stationary.
Anyone from NYC, especially around that time could tell you how obvious that none of the "Manhattan" scenes were actually filmed in any part of the real New York.
(at around 4 mins) Jim's mouth is out of sync when he says, "Gotta throw the anchor over".
During the rainstorm on the cruise ship the rain-making grid is visible in two shots.
(at around 27 mins) After Rennie sees Jason's child ghost the first time, she leaves her room and the camera pans down the hall to reveal Jason emerging from behind a door with a dartboard on it. Before Jason is shown, look into the pictures beyond the door and you'll see a crew member signaling for Jason to make his appearance. After Jason leaves the room you will see the crew members arm closing the door in the same pictures glass.
(at around 45 mins) When Rennie tries to lower the ship's anchor there is a member of the film crew among the machinery on the left.
(at around 29 mins) When Tamara pushes Rennie overboard, you can see a crewmember's hands reach out to catch her as she falls.
(at around 1h 20 mins) In the close-up shot of Jason standing behind the glass door on the subway, a crewmember is visible in the bottom left.
Geographically speaking, the cruise ship could not have traveled from Camp Crystal Lake all the way to the Atlantic Ocean.
When Jason was pulled down into the lake by Tina's psionically resurrected father at the end of Friday The 13th Part VII, the dock he was pulled through was near two houses, the remains of "Camp Forest Green" is nowhere to be seen, leaving us to assume it was cleared away years ago and new houses were built there while Jason was chained inert underwater. When Jim lowers the anchor that snags the powerline that resurrects Jason again, it appears Camp Crystal Lake is not only intact in the same location, but on the grid and running under its original name.
In Friday the 13th Part VII: The New Blood (1988), Jason's suit was shredded so much that you could see his spine and kneecaps. In this movie, he is wearing a new suit even though he was beneath the water for quite some time. He is also now wearing black gloves which he did not previously have.
(at around 16 mins) When the ship takes off we see some scenes with lots of people on board having fun playing, dancing, etc. But as soon as the killing starts the extras magically disappear and we are left with the main characters. At least after the fire alert starts the other passengers should be alarmed and rushing for the lifeboats. Surely Jason didn't just kill everybody off. Miss van Deusen is shown leading 4 extras (there were significantly more in earlier scenes) into the kitchen to wait. Later she mentions them and is told the kitchen is gone.
(at around 8 mins) The hockey mask Jason takes from Jim looks almost precisely the same as the mask he had previously (which was destroyed in Friday the 13th Part VII: The New Blood (1988)). It even has the same axe-gouge in the forehead.
As established in the previous films, Jason is just an instinctive killer who murders anyone he happens to encounter, when they're at the wrong place and wrong time. There should be no reason for him to have ignored the countless pedestrians and extras in New York just to keep chasing the survivors.
How did Jason follow the survivors from the cruise ship to the New York harbor? They had a lifeboat, he didn't, yet he arrives at almost the exact same time they did.
While Julius was an undefeated champion boxer, it makes no sense for him to one on one punching a guy in the face wearing a mask that is made to protect the wearer from flying objects like hockey pucks.
After Jason throws Wayne into the electrical switchboard, causing a fire to spread throughout the engine room, Jason hits the fire alarm. Considering Jason kills through stealth, that seems uncharacteristic of him to alert everyone of danger.