Plot hole: Andy is suspected of having killed Eddie Caputo, because he was at the scene when Eddie's house blew up and Eddie was killed. But there are glaring things that go unquestioned: None of the cops seem to think it's strange that a six-year-old kid would travel by himself so far to some random house in order to blow it up. The South Side neighborhood where Eddie lives is halfway across the city from Andy's apartment. How did Andy know where Eddie lived? How do the cops think he even knew Eddie at all? None of them address this most puzzling problem.
Suggested correction: The police believe Andy to be insane (hence why he is sent to a mental institution instead of juvenile hall), and thus do not believe his choice of victims to be in any way rational.
Also, as unlikely as it is that a six-year-old child could (or would) travel halfway across the city to murder a random person, the possibility that a child's doll came to life and carried out the act was considered far too outlandish at that point in the plot.
Continuity mistake: At the end, when Andy's mom shoots Chucky for the first time, it doesn't really faze him; he just keeps walking. But in the bedroom, when she shoots him through the heart, the bullet impact causes him to fly several feet through the air.
Suggested correction: Because shooting him in the heart is the only way to kill him, also when Mike Norris shot him he got sent flying, but when his body parts get shot off he still walks.
It has to be a human heart in order for him to die, that's what the man told Karen.
Plot hole: After Chucky electrocutes the psychiatrist at the hospital with Andy there witnessing it, all of a sudden Andy is at home on his own barricading himself in then hiding out waiting for Chucky to turn up. How did Andy get from the hospital to his home considering no adults were with him? (01:07:00 - 01:08:40)
Suggested correction: This is a question, not a plot hole. We already saw Andy made his way to Eddie's house on his own. We just aren't shown what he did to get home.