Continuity mistake: A sheet of paper and an inkpot miraculously appear by the automaton right after Hugo winds it up.
Factual error: The scene showing Paris at night displays heavy traffic and bright car headlights over the distance. Both were not possible to be seen at time the story occurs, circa 1920's.
Continuity mistake: When the automaton starts writing it stops the first time with the pen tip over a small figure made of three blocks. The shot switches to a rear view of the automaton and its elbow moves all the way back to the starting position. The shot changes back to the pen tip and it is still over the small, three-block figure. This is impossible as moving the elbow all the way back would have moved the pen away from the drawing.
Continuity mistake: When the monkey-wrench falls, it lays on the middle of two tiles. When the angle changes, it lays on the center of a tile.
Continuity mistake: When the automaton signs the drawing, it makes a dot inches away to the right of the "L". When Hugo hands the drawing to the lady, the dot is a thick mark right over the "L".
Continuity mistake: After the inspector saves Hugo, he yells at him "What were you thinking of?" Hugo's hair is moving wildly in one angle, still in the next angle, then wild, and finally back to still.
Continuity mistake: While the inspector flirts with Lissette, she is standing sideways or straight, depending on the angle.
Continuity mistake: When Hugo bumps into Labisse and the books fall, their position changes between shots.
Continuity mistake: When the drawings fly all over the room, the ones on the box's lid appear / disappear randomly between shots.
Continuity mistake: When the automaton signs the drawing, the tip of the "G" is under a line circling the moon's face. When the angle changes, the "G" is covering part of the moon's face.
Continuity mistake: When Isabelle chases Hugo at the station and falls on the floor, her position is inconsistent between shots.
Continuity mistake: After the automaton stops writing for the first time, Hugo steps backwards and faces it with his head positioned straight. A frame later it's tilted to the left.
Continuity mistake: When Isabelle hands the key to Hugo, the length of the string attached to it decreases between the first and second shot.
Continuity mistake: Lighting on the automaton changes between shots when Hugo uncovers it for the first time, notice the structure underneath: from hidden to visible.
Continuity mistake: Hugo tucks the beret covering his eyebrows, but a frame later it's above them.
Continuity mistake: When Uncle Claude shows up to deliver the bad news, Hugo turns around twice.
Continuity mistake: When Frick greets the lady for the first time, a waiter suddenly appears next to her in the second angle.
Continuity mistake: When Hugo leaves the notebook on the counter, it swaps from laying straight to skewed between shots.
Continuity mistake: At the toy-shop, Hugo empties his pocket and Méliès places his hand over the cloth and then takes it back. From the opposite angle, the hand is still over the cloth.
Continuity mistake: When Méliès shows up during the projection, Tabar turns around twice.
Answer: He's not making it a point to chase down random children - he's like a security officer at an airport. It's his job to apprehend thieves and troublemakers and keep the station safe, and he only threatens to send children to the orphanage if they don't have parents for him to return them to. Also, it's implied once he finally apprehends Hugo that his particular harshness toward orphans (and most of his character flaws in general) is due to apparently having been one himself. He spells out the kinds of lessons he was forced to learn by growing up without a family, explaining how he became so cold, bitter, and antisocial.