When Thom first tries to get rid of Captain by throwing her down the hall, he cheers with his right hand. When he watches himself on the camera, Thom is cheering with his left hand.
The babysitter's coat is buttoned up as she is about to sit down to watch TV, but it's wide open as she runs out the door.
The location of the envelope under the sideboard changes in different shots.
When Janie and Billy enter Mr. Popper's "snowy" home, Janie has the keys in her right and her left hand is in her coat's pocket. A few seconds later, she throws a snowball to her dad. But, in those seconds, she didn't bowed to take some snow for snowball.
Even penguin eggs must be kept warm to hatch. The movie implies otherwise.
When the penguins find Popper in the Guggenheim (about the halfway point), he is on the sixth floor (you can tell by the number on the elevator) of the eight story building. One penguin then causes a barrel of water and ice (roughly 40 gallons) to spill over, which they all use to slide down to the second floor, at which point they launch themselves to the first floor. The full length of the eight stories is 1,416 feet, of which they travel half, floor six to floor 2, or 708 feet. Since the spill is at least 3 feet wide (you can use evasive maneuvers and sizes of people they pass as an approximate measurement), that means the water and ice both must cover over 2100 square feet. But it would take almost 5000 gallons of water to cover that much square footage with at least 1/4 inch of water.
In the 1970s, Thomas Popper Jr. uses an amateur radio set to communicate with his father. It is operating around 21.2460 MHZ; however, during this time period, this was not an available voice frequency to American amateurs.