In the opening scene, the plane externally is a Boeing 737-700 and when the camera zooms into the windows looking in, you can see that the seating arrangement is 3 seats an aisle and 3 more seats - the normal configuration for this aircraft. However when the camera zooms inside the aircraft, the cabin layout is much bigger with a 3-3-3 seat layout and dual aisles. The only twin engine aircraft that Boeing has that could match this seat configuration is the Boeing 777. At the end of the scene just as the plane is landing in the sunset, a completely different aircraft - a Boeing 767 is shown landing.
When Sergei dies, he drops the microwave gun right underneath the alien that 'dusted' him, however, just a moment later, Ben picks it up as it is now laying at his own feet and now has a blue, a red, a green and a yellow light on it. Towards the end, just before jumping into the river, the original microwave gun with the timer dial on the side returns.
The radio that the group finds in the US embassy works because it was protected from the EMP strike inside the bird cage which acted like a Faraday cage. A Faraday cage blocks EM waves, including microwaves. The radio works in the bird cage because the antenna is connected to a wire leading outside of the cage; but it would not have worked in Sergei's apartment.
In the mall, Sean discovers that the aliens cant see them through glass since they are reading the human bio-electrical pulses and glass does not conduct electricity. So the bulb on Sean's neck shouldn't be lighting up either.
Toward the end of the film when the characters have to jump off the boat into the river, Sean and Natalie both jump in together holding hands. All the characters except Natalie emerge together and climb aboard the submarine. Somehow Natalie has managed to end up in the city, clearly more than a few kilometers away.
When they are floating down the river on the boat to get to the submarine, you can clearly see the footage is reversed to make it look like the boat is floating down the stream. The sailing route is clearly visible, and the boat is "floating" backwards along it.