During Charlie's date with Eleanor Skepple, there is a shot with the camera over Charlie's left shoulder right before he says, "Get physical." During the over-the-shoulder shot, Charlie is holding a shot glass in his right hand. As he drinks it, the next shot showing Charlie facing the camera has him lowering the same shot glass from his mouth, but it is now in his left hand.
Charlie helps jump start Cam's car, and locks the keys in the car. Charlie drives her home to grab her extra pair of keys. When they return, the car is off and the remote on the extra pair of keys allows her to unlock the car. The car was left on when they left because she couldn't get back into the car. In addition, Toyotas will not work with the remote if the car is running.
The goof item below may give away important plot points.
Chuck couldn't casually book an air ticket to Antarctica as he did in the movie. The only way to fly to Antarctica from the U.S. is to pre-book a flight through a charter service or a paramilitary organization like the New York Air National Guard. Even if he did that, he would never make the connecting flight to Antarctica because he would never pass a strict gear check.
Cam would not be able to fly to Antarctica for a week. A typical stay for a researcher in Antarctica is at least six months because the window of opportunity for planes to land there is very short. Flying back and forth would take at least a week.