(at around 39 mins) After leaving the baseball park the group hop on a train which goes into the subway. On the train are several passengers. Two of the female passengers on the train are also waiting at the following subway platform at the exact same time. They're even wearing the same clothes.
During the film's opening credits montage, buildings One and Four of the current (rebuilt) World Trade Center appear under construction. Later, as Ellen and Mora Brody are riding the ferry to Liberty Island (as well as various shots of Lower Manhattan shown throughout the rest of the film), both buildings are seen structurally complete.
(at around 1h 17 mins) After April sawed the shark on the roof, her hand saw is covered in blood. The next time you see her, it is clean as new.
(at around 1 min) When Skye runs across the roof with a paper bag with the Yolo' B' Us logo on one side, the logo changes sides several times.
(at around 45 mins) When the three women are running from the Statue of Liberty's head, as it bowls down the road, they jump into, and start driving, a rubbish truck. Despite taking off in the same direction, they then drive down the same street they've just run down, with the statue's head rolling past the same cars it's already missed once - it must have done a complete circuit of the block.
(at around 7 mins) Despite the fact that the airplane would have depressurized as soon as the first hole appeared in the plane, the air masks never deployed.
(at around 40 mins) When on the metro after pushing the emergency break the people fall the wrong way.
The plane has 4 engines and only 2 throttles.
The cockpit on a 747 is on the upper deck. This one is on the lower deck.
(at around 39 mins) The metro train would not receive electricity from the tracks if they were flooded.
(at around 1h 15 mins) When Fin saws the shark in half on the fire truck, blood is spills from the shark yet there is not blood on him, the chainsaw, or the truck.
During the plane scene, camera shots from outside the plane show an elderly man sat in the seat behind Fin. But any shot from inside the plane show an elderly woman sat in that place.
(at around 9 mins) There is a hole in the cockpit but Fin's hair and clothing never demonstrates any evidence of the wind that would be blowing in the cockpit.
(at around 1h 6 mins) When catapulting the bombs into a sharknado, the bombs aren't reflected in the window.
(at around 1h 17 mins) When Skye yanks the wires out of the freon tank they spark showing they are live. When she connects the alligator clamps to them and tells Fin she's ready, the clamps are touching, if it were live, it would trip the circuit breaker immediately.
(at around 27 mins) The retired baseball player tells Ray that his father was sitting in a particular section of Citi Field at his final game twenty-five years previously, which would have been 1989. Citi Field did not open until 2009; at the time of the player's last game, the Mets would have been playing in Shea Stadium.
In the sequence before the explosion on the Empire State Building, crew members and the green screen are clearly reflected in the window behind Fin.
(at around 40 mins) The 7 Train does not run on 96th Street line. 96th Street is closer to Yankee Stadium than CitiField.
(at around 15 mins) It is only reported that there are only several injuries from the plane crash in the beginning when due to the loss of the pilots and the loss of part of the fuselage wall there were also at least four fatalities.
Since the Today Show is on the air as the same time as the Mets game, the baseball game would have had to start before 9 am.
When Fin is on the roof of the hotel he sets the sword down on the roof. When he runs back into the building he does not take the sword yet he he has it later fighting sharks.
(at around 55 mins) Fin says that flooding is causing sinkholes. This is impossible as Manhattan is solid bedrock.
When the 4-engine 747 loses one engine, the pilot calls, 'MAYDAY-MAYDAY!' The loss of one engine hardly constitutes a dire emergency. But if the Pilot felt it was necessary, he'd call 'PAN-PAN', the international call indicating a problem, wish to land with priority but not require immediate action.