In every scene filmed in the basement of Jesse's house, the basement door opens into the room. During the last scene in the room, the camera pans to the door but it opens out into the hall.
Multiple characters routinely wear the same outfits in scenes that are supposed to be happening on different days.
When leaving the pool party, Jesse is wearing the same clothes that he was wearing when Coach Schneider was killed. Jesse was found naked by the police, so couldn't have got them back. If left there, they would likely have been taken by the police as evidence, so there's no way he could still be in possession of them.
(at around 3 mins) In the opening scene text on the school bus varies between SCHOOLBUS and SCHOOL BUS.
(at around 29 mins) The broom that Jesse's dad is holding while the bird is flying around disappears.
Elm Street's setting in Ohio isn't confirmed until Freddy's Dead: The Final Nightmare (1991). Therefore, at this point in the series it could be meant to be in a state where palm streets grow. Also, the desert scenes only occur in nightmares, and thus free from realism.
Near the beginning of the movie when the Walsh family is eating breakfast, Ken calls his wife "Mom". It's not unusual for husbands to call their wives "Mom" in front of the kids, particularly young children like Angela.
There is an instance in which the same scene is used twice: after the gym fight when Grady and Jesse are holding the push-ups pose in the field, as punishment (at around 10 mins). This is the same scene used for when Jesse insults Schneider in the locker room (at around 28 minutes). The same people pass behind the fence.
(at around 21 mins) When the kids are reading the diary about Freddy Krueger, the pages that they are "reading" from are all blank.
(at around 29 mins) During the scene with the parakeet, first it knocks over a lamp and then the father breaks the other lamp. The room never gets any darker.
(at around 1h 7 mins) When Freddy Krueger jumps through a glass door and disappears mid-jump, at the point he vanishes, so do several pieces of the door's debris. Clearly there were two takes, one with Freddy jumping, one without, and they simply faded between them. This is very noticeable if you look at the door pieces at the top left of frame.
Coach Schneider is supposedly stripped naked before he is whipped. However, in one shot he is still wearing pants. This is only noticeable in full-frame video versions.
When Jesse and Lisa are reading the diary left behind by Nancy from the previous film, they read that Nancy is aware of Fred Kruger's name before her friend Tina is killed. However, in the first film, Nancy only finds out Fred Kruger's name after Tina's death.
In the opening scene when the bus is coming down the street, one of the crew members is visible walking back and forth behind a tree on the left side of the screen.
(at around 34 mins) Behind the tennis racket on the wall, you can see the heating element that's lighting up and burning the strings in two.
During the opening credit scene, when the bus drops off the students and then drives off, the reflections of the camera crew and crane are visible in the bus windows.
In the first movie, Marge Thompson states that Krueger took his victims to an old abandoned boiler room. In this movie Lisa states that he worked there, meaning it couldn't have been abandoned.
Coach Schneider was murdered on the same night Jessie was picked up by the police, naked. Being that they would have had a record of this, it would seem likely that Jessie would be a suspect or at least a person of interest in the murder.
When Jesse is unpacking in his room and he turns on music, he presses the "FF" button instead of the "Play" button.
When Jesse goes into the club, and sees the Coach there, the Coach would have known that Jesse was a underage minor. It's implied that he is anywhere from 16-18. Not only does this make the next scene impossible, but even in 80's, he would have likely has his id checked, and would have never gotten into the club, as depicted and he was way to young to be there.