At the 1hr 11 min mark, Nancy tells her father "to break the door down in exactly 20 minutes" at 12:30 am, making the current time 12:10 am.
In this time, she manages to set various booby traps--a bomb from a light bulb and gunpowder, a raised sledgehammer, a tripwire, and screwing a bolt to a door, and then sits with her mother for some time before going to her own bedroom. All of this was apparently done in only 10 minutes! She's shown in bed at 12:20 am, giving herself 10 minutes to fall asleep and catch Freddy.
(at around 1h 15 mins) When Nancy checks her watch she is wearing a short-sleeved nightgown, but the close-up shows a wrist with the end of a long blue sleeve on it.
(at around 28 mins) To wake herself up, Nancy smashes the outside of her arm against the boiler. But when she wakes up, the burn mark is on the inside of her wrist.
(at around 23 mins) The person who gets up to speak in the classroom is not the same person who was sitting in the same seat in the establishing shot a few seconds earlier.
(at around 37 mins) When Glen is watching over Nancy while she sleeps, the lamp is turned off, darkening the entire room. When she wakes up from her nightmare, her bedroom light is turned on, lighting the entire room. This mistake is digitally fixed in the 2006 Infinifilm release of the film.
When Nancy breaks the jar of gasoline on Freddy's chest and lights him on fire, the fire is burning everywhere except where the gasoline was.
Everyone thinks Rod's death is a suicide. Since suicide's considered unforgivable by the Church, a Catholic priest wouldn't be presiding over his funeral.
In the full-screen version, during the first nightmare sequence right before Freddy pops up to scare Tina, you can see Robert Englund as Freddy crouched down and moving into place behind her; however, at the time of the film's release, director Wes Craven would assume that only the wide-screen version would eventually be available for home viewing. You can't see Englund behind Tina in the wide-screen version.
When Rod Lane is arrested, he is not wearing a shirt under his leather jacket. However, a short time later when Nancy visits him at his cell, he is wearing a shirt under the jacket. It is obvious that the police provided him with a shirt.
When Nancy smashes Freddy's head on the coffee pot, she takes the pot off the top of the TV -- but that was the coffee pot that her mom already took off of her TV.
At a later point, Nancy's mom pops into her daughter's bedroom to see that she's going to sleep. An instant after she leaves, Nancy pulls out a pot of brewed coffee (brewed as indicated by a red light lit on the machine), yet her mother fails to smell it. However, when her mother leaves the room, she takes an old coffee pot and several mugs with her. She might have assumed any coffee smell came from them.
Elm Street's location in Ohio isn't established until Freddy's Dead: The Final Nightmare (1991). Therefore, at this point in the series it isn't a goof if Glen's car has a California license plate and palm trees are seen around town.
(at around 1h 20 mins) Crash mat visible when Nancy jumps out of the boiler room and lands in her lawn.
(at around 51 mins) When Nancy is in the kitchen with her mother after the visit to the dream institute, she walks in and drinks coffee from a mug; however, she clearly isn't drinking anything since she isn't swallowing.
(at around 16 mins) When Freddy scrapes his claws with his arms elongated while chasing Nancy down the lane, you can clearly see the skin under his glove is normal. Anyone who was burned to death would be scarred from head to toe.
(at around 16 mins) Freddy intimidates Tina by slitting off his own pinkie and ring fingers, but blood only spurts from the pinkie.
When Nancy talks to Rod in jail, he still has quite a bit of blood on his hand (and no visible cuts). When the police arrested him, they would have made sure he got cleaned up, just like they got him a shirt and shoes.
After Freddy falls down the stairs, the knife on his pinky finger isn't there and shows up in the next shot.
(at around 34 mins) When Nancy watches The Evil Dead (1981) on TV, the scene playing is from the end of the film; however, the screaming heard during the scene is from the famous "Tree Rape" scene, a scene which happens near the beginning of the film.
When Nancy wakes from her nightmare in the Katja institute, the nurse approaches her with a syringe and says "this will help you sleep", but the nurses mouth isn't moving.
(at around 22 mins) When Rod is cornered by the police, he stops and raises his hands and you hear him say "I'm cool, I'm cool", but his mouth clearly isn't moving.
Around 10 min in, Glenn is looking outside for a strange noise and you see a crew member's jeans on the right edge of the screen.
Nancy burns herself with the pipe to wake herself up from the dream, making it seem like pain will cause the dreaming person to wake up.
However, when Tina (and any other victim) is cut by Freddy's claws the pain does not wake her up.
It is established in A Nightmare On Elm Street 3, that every teenager has the ability to enter dreams and have superhuman like powers. Yet, in this film the teenagers seem to not have these abilities and this was clearly created later. As the original film is more grounded and more realistic, despite the supernatural elements. Nancy and all of the teenagers should have had dream powers, and should have been able to fight Freddy in his own world.
(at around 16 mins) Throughout the movie, along with all the sequels, Freddy's "razor" glove is on his right hand. When Freddy is chasing Tina, there is a quick shot of him jumping out from behind a small tree and his glove is on his left hand.
When the police found Rod hanging from the prison cell, he had only been hanging for a short time. They should have tried CPR to save him instead of giving up and pronouncing him dead right away.