Revealing mistake: When Chucky's disembodied head tries to bite Andy in the beginning, watch closely. When the plaque he's mounted too leans forward suddenly as Chucky snaps at Andy, you can see a rod underneath of it, which was used to make it move and lean forward by the puppeteers.
Revealing mistake: When there's a close-up of the needle going into Nica's arm, you can tell it's a fake needle - the tip is just flat, and there's no hole, unlike a real hypodermic needle. You can also spot where the fake needle "retracted" in the center.
Revealing mistake: When Claire is bitten by Chucky and she pulls her sleeve up, you can see where the prosthetic is blended into her arm in the first wide-shot. In both that shot, and another shot, you can also see the prosthetic unnaturally "bulging" slightly. It's also very visible in the scene where she's strapped down and Dr. Foley injects her.
Answer: It's been years since the injury. Maybe she transferred her soul to another doll? Maybe she repaired her head? Maybe she copied her soul into another pristine doll as she can now inhabit multiple hosts at once? Take your pick, as it's a relatively insignificant matter.
TedStixon