Deliberate mistake: In the handyman's room, we see he has cameras secretly set up in the various apartments to spy on neighbors. But the placement of the camera spying on Mrs. Norris' dining room is kind-of ridiculous. It appears to be sitting out in the open on her dining room table. Sure, the handyman is a pervert, but there's no way he could get a camera onto such a spot without it being totally obvious.
Plot hole: The Vietnamese sweatshop is structured in a way that makes no real sense: the workers seem to be randomly in charge of everything and nothing instead of having specialized, streamlined tasks. Already makes no sense that a low level employee would be able to reprogram a state of the art AI chip, it makes even less sense from a production standpoint that he'd also be given a disassembled doll, dress it, etc.
Deliberate mistake: When the creepy building handyman falls onto the table-saw, it slices what appears to be his leg (or possibly arm) clean off. Except the saw-blade wasn't big enough to go right through his entire thigh (or upper arm for that matter), though... it only sticks up a few inches.
Plot hole: Karen forbids her son from playing with Chucky, because he's spending too much time with it on top of it scaring the cat, and locks it up in a cabinet. The cabinet ends up broken (Chucky broke it but she does not know), the cat conveniently disappears (Chucky killed it but she does not know), but the mother is totally cool about it, the plot point is forgotten and Andy faces no punishment or questioning for it. Any mother would be alarmed and would make a big deal of it possibly even throwing the doll away (she does not care, she did not pay for it), but that sort of drama is delayed until much later in the movie, for no internal reason.
Plot hole: Since the "Buddi" doll is designed simply to be a child's toy, able at most to carry items like a book or a banana, and Chucky in this movie is not a supernatural creature, it's hard to explain how it is strong enough to, for instance, carry the heavy watermelon across town and lift it in position. Even if his safety locks have been removed, a toy designed to be in the crib with toddlers wouldn't be built with the kind of lifting power shown here (we also see it assembled and it does not have a terminator skeleton or something like that, it's mostly plastic).
Continuity mistake: When Chucky is controlling the car with the police officer's mother inside of it, pay attention when she says the line "You hobbit, mother****er!" In that shot, she doesn't have her seatbelt on. However, both before and after this shot, she has her seatbelt on. (It doesn't get taken off until a few shots later).
Continuity mistake: After setting his mother free from the forklift, Andy grabs the knife and stabs Chucky in his power core, shutting him down. Moments later Chucky lunges towards him only to be shot by Detective Norris and the hole is no longer in his outfit. (01:21:03 - 01:21:44)
Continuity mistake: Having dinner at the mom of Detective Mike's, look at Mike's hand when she gets up saying "That's all." His hand is suddenly raised, eating, while they were both down and empty in the previous shot. Similarly a moment later Andy gives a nervous look to the gift, fork vertical - but he's eating in the following shot. (00:51:20)