The deadbolt on the door in the beginning keeps changing from horizontal to about 45 degrees every time the camera zooms in and out.
When John and Jill go back to Julia's apartment after she had been shot, there is fingerprint powder on the door and door locks. But when they go into the apartment, there are no more signs of fingerprint powder on any surface. Standard procedure would dictate checking the entire apartment for fingerprints.
Its stated that Julia was asked at the last minute to babysit. If so, why did Landis have the whole scenario planned for that night? He would not know she was going to be there.
Jill Johnson had a husband and two kids in the original film, in the following years after she had been terrorized by the killer in the opening scene. This family of hers never appears in this film, nor are they mentioned either, and it appears that she lives alone in her apartment as well.