(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.
(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.
(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.
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 39 mins) Besides the two women already mentioned that are on the train and on the platform, there is also an older gentleman who is standing on the platform wearing a hat and beige coat who is also one of the first people seen running through the door after the shark gets the policeman on the train.
(at around 4 mins) After Fin sees the first shark when looking out the plane window he slams the window shade down. The very next shot shows the shade open, but the next time Fin looks out the window he has to open the shade first.
Matt Lauer alludes to it being "July" and the Mets appear to be playing a regularly scheduled game. The characters state several times that the weather is "crazy" but that does not adequately explain trees with and without leaves in several shots, piles of snow in the streets and occasional visible breath.
(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.
(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.