When both the Tramp and the Kid are chased by the policeman, the Kid loses his cap, which falls to the ground in the yard before he enters his home. Still, when he is seen inside, he has got his cap back on his head.
The Bully punches through a brick wall, but the damage pattern changes in later shots.
When the Woman is giving toys to the children on the street, she sits down on the curb and a woman hands her a baby. When she takes the baby, she sets the last two toys, a dog and a ball, next to her on the curb and the ball rolls off the curb, out of shot. A few shots later, when she meets John, the ball is back in position, beside her. She picks up both toys and gives them to him.
During the fight scene with the Bully, the unconscious police man on the ground changes position in between shots.
After John has made pancakes and the Tramp gets out of bed, a kettle can be seen on the corner of the table. After the Tramp has put a chair next to it and goes to sit on it, in the next closeup shot of them on the table, the kettle is missing.
When The Tramp and The Bully fight, The Bully takes an attempt to swing his fist at the sign. Despite this being the case, no actual contact with the sign was made, and it appears that the sign moved on its own.
The Bully made to attempt to hit the sign, which was about 2 feet above his head. He was clearly aiming for The Tramp's head. This was a probably a sight gag, suggesting that his punch was so powerful that it created a wind (like the trick of blowing out a candle with the rush of air from a punch).
On the rooftop, after the Tramp chases the two welfare workers who have captured and tormented John, the scene ends with the Tramp and one of the workers fighting on the back of the workers' pickup truck. After kicking the second welfare man off the back of the pickup, the Tramp makes a 'nonsensical' wave good-bye as he and John ride off to momentary safety. In reality Charles Chaplin (also the director) is waving 'CUT' to cameraman Roland Totheroh.
When the Bully (Charles Reisner ) "punches" the lamppost in half during the fight with the Tramp, the post begins to bend itself an instant before the punch lands on it.
The Bully's brother (played by Raymond Lee) clearly has fake muscles. (This is a 1921 movie and, therefore, they didn't have sophisticated resources, but they should have cast an actor who was truly strong.)
The reward notice for the lost child lists "H. Grafton" as Chief of Police but the article just below it mentions "N.W. Stephenson" as Chief of Police. To be fair, on release, audiences would not have had a chance to read the details. (The rest of the text is similarly disjointed, as if different articles have been randomly pasted together.)
When the doctor hands the note to the woman who is wearing white gloves, the hand holding it in the closeup is not.