In the chase scene with the taxicab and Audi stuck together, you see Holbrooke's Audi smash into several cars. If you pay close attention, you can see that the left front tire and wheel is destroyed after impact. In the very next scene, the Audi is seen with all four wheels intact. The same thing occurs a bit earlier in the scene, with the right rear tire and wheel being destroyed.
Holbrooke Grant makes reference to driving "up and down the Turnpike", looking for real estate with Claire Foster in Upstate New York. New York State has a Thruway that runs north of New York City, but there are no turnpikes Upstate.
When Claire and Phil return in disguise to "Claw Restaurant", Phil is wearing Claire's glasses. Because of this, she needs to look extremely close to the electronic display at the hostess station to retrieve a telephone number. However, after Phil and Claire break into the competing realtor's office, Claire retrieves a telephone number a few feet away from the computer monitor, still not wearing her glasses.
After they came out of Central Park, Claire thought Phil was vomiting blood. Phil replied that it was the Cabernet he drank at dinner. An earlier scene actually showed the waiter serving them a bottle of Bertani Amarone, a northern Italian wine which contained no Cabernet.
During the scene where Phil is puking in the street after running from the 2 thugs. The are several bystanders that walk by multiple times in both directions. Specifically with 2 women in the blue shirts.
In the rooftop scene towards the end of the film, the detective tells the cops to take the DA and Joe Miletto away, in this scene you see her face and their heads turning as they are being led away. However, in the next shot the DA is still facing her. This also happens again when Collins and Armstrong are being led away, in the first shot you them turn but in the next one Collins is still looking at the detective.
In the scene where Phil and Claire are preparing for bedtime the clock can be seen to be displaying 10:58 as Phil climbs into bed. As the scene ends, the clock still displays 10:58 despite the scene lasting well over a minute.
The boat that Phil and Claire escape on in Central Park has a registration number that begins with the letters "CF", which indicates that the boat is actually registered in California. New York state boat registration numbers begin with the letters "NY".
After Carell's character lands in the water, after the Audi/Taxi chase under FDR highway, we see the South Street Seaport lights in the background, far to the south. The distance of those lights -- along with the design of the river walk barriers -- indicate he probably was swimming near the Brooklyn Bridge or Manhattan Bridge.
In the following scene, however, he and Fey's characters are shown on the #1 subway train, which can only be caught FAR AWAY from this location. If they'd first taken a different train in order to transfer to the #1, they must have done so in total silence.
The Fosters 'borrow' Holbrooke Grant's Audi and drive to 135 Avenue D (the real Tripplehorn apartment). In the ensuing driving/chase scene, mere blocks after the chase begins they pass a very conspicuous awning reading "226 West 9th Street." Moments later, they drive on a Manhattan Avenue, passing a street sign for "Spring Street." Such a driven journey would be impossible in the elapsed movie-time.
In the scene where the Audi is stuck to the cab the two cops shoot out the front window of the Audi. The window shatters when the bullet hits it. Front windshields are made out of laminated safety glass and do not shatter.
The cabbie provides a Kindle to view data which is stored on a USB flash drive. The Kindle's only USB port is a mini-USB-B port, which is both the wrong size and the wrong type of USB port to accept a flash drive.
In the chase scene, the black police car, driven by the bad cops chasing the Fosters, is shown with blue and red lights on the front. This is a mistake, as it is illegal for police in the state of New York to have forward-facing blue lights.
While eating dinner, Claire walks over to take a picture with Will.i.am, his hands are across the table between two glasses. When the pictured is shown, his hands are close to his mouth and the glasses are far apart
At the end of the chase scene (right before the Audi and the cab are separated by the Suburban), the connected cars take a right around a corner. Watch closely - the rear wheels of the cab turn, making the stunt possible.
The goof item below may give away important plot points.
In the final showdown on the roof, the show-down is interrupted by a police helicopter ascending from below the roof.
The club ("The Pink Hippo") seems to be about four stories tall (with a street level entrance) and exterior shots show it to be located near or below 23rd street, just a few blocks from the Manhattan waterfront. There are no buildings tall enough in this area to allow for any such "surprise entrance" from below by a helicopter, even ignoring the audio disturbance such a presence would cause.