When Junior drives the family car into the glass at Big Ben's, just before he gets to the glass, a pickup truck backs out in front of the Healy family car. It conveniently disappears and is forgotten mere seconds later.
When he falls off the trapeze, the Bow Tie Killer falls into a tiger cage that was not down there before. In fact, just mere seconds later, Junior slides down the rope below the trapeze poles, into his father's arms.
All throughout the movie, Junior has all his baby teeth, and longer hair, and then looks a little older with shorter hair and a large top front tooth growing in. This happens within scenes, beginning in the orphanage.
At the last scene on the bridge, after Ben got shot, you can see the wheel of the overturned car turning in some frames and then be completely still the next, and then moving again a few seconds later.
When Junior sends Martin a letter in prison saying he's getting out of the orphanage, he didn't know at the time that he was getting adopted by the Healys and Martin had escaped from prison the day Junior went home with the Healys. So how could Martin have known where the Healys were living and that Junior was staying there?
When Ben is standing on the bridge watching the truck drive away with his wife in the back, he has the rifle in his hand. Ben and Junior turn around to walk back to the car and the rifle disappears. It seems unlikely he would have left it laying on the bridge.
When a piece of meat falls on Mother Superior, it falls on her nose and sticks to it. However, in the next shot, when she removes the piece, her forehead and her gown under her neck are also spotted. Then she takes Junior out of the canteen and her gown is clean, and in the next shot, it is dirty again.
As the car is entering the store through the front glass there is a shot with a reflection of the car. Rigging can be seen on the vehicle, and it looks to be a different type of vehicle all together than what we see in the next shot.
When Junior crashes the car into the glass enclosure, while Ben is on the roof of the car, it's obvious that John Ritter has been switched out for a dummy, as evidenced by the stillness of the body, as the hundreds of tennis balls crash down on him.