(at around 40 mins) When Carol-Anne hangs up the phone and walks to her bedroom, the light switch on the wall changes from 'off' to 'on' between shot angles.
(at around 1h 15 mins) When Pat and Bruce are in the garage being chased by the cars covered in ice and snow, the cars pull out to face them and you can see that the windscreens on the cars have tiny spy holes for the drivers to see through but in the next shot when the cars are still and parked, the spy holes have been covered up.
(at around 26 mins) When Bruce and Patricia are shown in their room from outside the window, Bruce's black suit is laying on the end of the bed. Two shots later when they are shown from inside the room, Bruce goes to sit on the bed and the black suit is now laying in a different position on the bed.
(at around 1h 22 mins) When Bruce and Patricia are crawling out of the elevator, Bruce's legs are still inside the elevator as he helps Patricia out of it. The shot changes, and his legs are out. It changes again, and his legs are back in.
(at around 22 mins) When Doctor Seaton is hypnotizing Carol Anne, he puts his hand on her face to calm her down. When she does, her head slants. In the next shot of her, her head is dead centered.
(at around 1h 8 mins) When Doctor Seaton is pushed down the elevator shaft the elevator is shown going up with the floor doors open and the doctor sprawled on top near the door operator. This would never happen because elevators are equipped with door interlock mechanisms. This means the outer doors (floor doors) could not be opened unless the elevator is present and completes a circuit. This mechanism also cuts the circuit to prevent it from moving if ANY doors are open. These multiple redundant fail-safes have been around for decades and would certainly be available on an 1988 elevator within a building portrayed to be a state of the art, new construction.
In the end sequence, you can see that one of the mirrors is fake, by having cables run floor to ceiling to simulate the seams. Nancy Allen bumps into the cable and it rattles when her mirror image startles her, she bumps in the cable and you can see it vibrate.
(at around 44 mins) When Carol Anne escapes the stairwell, her hair seems to defy gravity, indicating that the shot was filmed in reverse.
(at around 47 mins) When Carol Anne is pulled into the puddle in the parking garage, the platform she is standing on is visible.
(at around 1h 16 mins) When Bruce Gardner and Patricia Wilson-Gardner are being chased by cars in the underground garage the driver is visible when one of the cars is crashed at the end of the chase.
(at around 1h 21 mins) In the elevator sequence, when Bruce is trying to reach the buttons for second time, in a shot, a wooden plank can be seen.
Carol Anne is far too old to be playing with a Speak-N-Spell-she would have been too old for such a toy in the first movie, in fact. As a gifted child who clearly knows how to read already, she would have no need for such a thing.
(at around 32 mins) After something strange happens in the bathroom as Donna gets ready for a party, Carol Anne and Donna walk into the main hall of the apartment. In the back, there is a large mirror. In the bottom, right-hand corner of the mirror, a crew member's bottom is shown wearing sandy brown dress pants.
(at around 52 mins) When Bruce is thrown across the room by the fake Carol Anne (when he reaches Carol Anne's bedroom door), Pat yells out, "Tom!"