Plot hole: The TV-watching girl is killed when Freddy shoves her face first into a TV set. (one of the more creative movie deaths.) But the thing is, all the other deaths have been set up to look like suicides if not accidents - this one was obviously foul play, since there's no way she could have launched herself into the glass of a TV screen hard enough to break it. We see that her body is found this way, but they make no inquiry.
Suggested correction: Not all of the deaths were meant to be suicidal; Phillip and Kirsten were the only exceptions. When Will and Taryn were killed, it was in the dream when they wanted to help Kirsten but nobody was there to witness it and it was much later in the film. Also when Joey was caught by Freddy, he was only passed out but still alive. The one kid that cut his eyelids off was not only never shown but his death happened by his own doings out of fear for Freddy.
It doesn't matter if Jennifer's death wasn't intended to look like a suicide - she is in a locked ward and was the victim of a homicide. Yet there's no investigation.
Why would there be an investigation? Especially when she was the only one in the room - apart from Freddy - or maybe there were cameras there?
Plot hole: When Angel comes back to the doctor's home with food, he opens the bedroom door and turns on the light in that room. The lights are already on outside this room when we see him turn the doorknob. When Angel leaves, he leaves the light on in the bedroom and heads downstairs. Just before leaving out the front door, he turns off the light switch nearby. The shots changes to show the doc's body and the room going dark- as if Angel is still in the bedroom and turned off that light. (00:23:10)
Plot hole: After Margaret kills Mike at the end, she leaves through the door that is right next to his corpse, leaving her fingerprints on it, since she is not wearing any gloves. Under these circumstances, the police surely would have done some forensic investigation and dusted the doorknob for prints, which would lead back to her. Considering Margaret moved up from being a psychiatrist to a lively con criminal, you'd think it would occur to her to clean up a little bit, but she gets a happy ending.
Suggested correction: As she tells Mike, she's out of control. I don't think she planned to kill him, but he goads her into it by telling her she really hadn't learned anything and he played her. THAT was the point she learned the lesson. She took the risk and killed him. The doorknob fingerprints were a risk, but not much of one since a lot of people probably used that door before the police got there.
As for many people using the door after the murder, probably only one person might have used it if they opened it from the hallway side, only touching the hall side knob. That person would have immediately seen the body and called the police. Anyone on the baggage handling side wouldn't have touched the doorknob. Still, Margaret is not in much peril from fingerprints, since we are led to believe she has always been a "good person" who would probably never have had her fingerprints taken.