(at around 34 mins) When Nancy is watching The Evil Dead. The scene playing on the TV 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.
(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 Nancy is going up the stairs and steps into the marshmallow goo, you can see a visible mark in the goo where Nancy is supposed to step so her foot does not get misplaced and to know when she can take it out.
When the cops are running through the house to go downstairs because Nancy called for them, the fire of Freddy's footprints are not on fire. But in the next shot where Nancy is running up to get her mother, the fire is up and burning since Freddy walked up to the upstairs.
(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.
(at around 1h 20 mins) When Freddy appears after Nancy yells at him to come out and show himself, he is wearing his hat. Previously, Nancy had pulled Freddy's hat out of her dream at the clinic. In the next scene, as Nancy is being chased down the staircase by Freddy, his hat has disappeared.
(at around 22 mins) When Nancy is by the bush with Rod, his hand and chest are covered with blood, but when he runs out and is surrounded by the police, which is supposed to be moments later, his chest is clean.
(at around 56 mins) In a wide shot, when the bars have just been put on the house, the front door window bars are different than the close-up of Nancy on her porch. The closer shot shows a heart shaped design rather than the three-bar pattern of the wide shot.
(at around 1h 16 mins) When Nancy is asleep and looking for Freddy she goes down into her basement. After finding Freddy's claw is missing she opens a door leading to Freddy's boiler room, by pulling it towards her. The camera cuts to the other side of the door is facing the other way, as if it was pushed open and not pulled.
After Rod is arrested and Nancy walks away from her father, you can clearly see her drop her blue bag in a bush; then the movie hard cuts to a shot from the exact same angle, but now her bag is back under her armpit again.
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 Robert Englund behind Tina in the wide-screen version.
It is revealed in the movie from Nancy's dreams that if she is holding onto something in the dream world, like an object or person, she can bring that object or person into the real world from the dream world. This is shown in the movie's climax. However Nancy was clearly holding onto Freddy when she went to find him with Glen guarding (and not succeeding) in her bedroom earlier in the film. She was struggling with Freddy and holding onto his razors to keep him from killing her in the dream world and was awoken in the exact same way as in the climax, from an alarm. Why didn't Freddy get pulled into the real world at this point?
(at around 33 mins) Obvious stunt double for Nancy when she is pulled underwater. The double also has blonde hair. (In the audio commentary actress Heather Langenkamp is watching this scene, and she embarrassingly says, "That is not me!")
(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) While Freddy scrapes his claws while his arms are 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 the end of the final dream in which Nancy brings Freddy back into the real world, she is wearing an alarm clock wrist watch, letting her know that midnight is approaching. When she awakens in her bed, she is not wearing one.
(at around 20 mins) The morning after Tina dies, Nancy's mother, Marge, is pouring herself a drink. After Marge turns off the TV, you can see her bottle of liquor on the counter as Nancy walks to the door. The camera then cuts to close-ups of the two women, then goes back to the wide shot and the bottle is gone from the counter.
(at around 1h 23 mins) After Nancy sets Freddy on fire, she goes running up the basement steps and out the door but she leaves the door open, and it is still open as Freddy is coming up the stairs, but yet when he reaches the top, Nancy opens it and knocks him back down without having closed it in the previous shot.
During her nightmare in the dream clinic, Nancy pulls Freddy's hat out of her dream and into reality. Later during Nancy's final nightmare, Freddy grabs her suddenly, and for that one brief shot is wearing his hat, then he remains hatless for the rest of the film.
(at around 17 mins) When Tina is killed, her shirt is ripped open and her chest is cut by Freddy's four blades. In the next shot she is pulled up the wall then onto the ceiling and her shirt is buttoned up.
(at around 1h 8 mins) When Glen is just about to be killed, we hear the radio announcer saying that "it's twelve midnight". But when he is being dragged into the bed by Freddy, the clock beside his bed shows 11:52. However, since the radio announcer also gives the station call-sign as "KRGR" ("Krueger" minus the vowels), the time may be midnight only in Glen's dream.
Towards the end of the movie, Nancy was about to go home and go to sleep so she could bring Freddy back with her. She told her dad to come break down the door in exactly 20 minutes so he could get Freddy. In the 20 minutes before she was scheduled to wake up from her dreams, she was able to string up all those booby traps and have a heartwarming talk with her mother and then proceed to fall asleep to go get Freddy. That seems highly impossible.
(at around 1h 22 mins) While Freddy is chasing Nancy down the stairs after the sledgehammer hits him, he falls down form the top of the stairs. When he falls, you can clearly see Freddy land on a bed to break his fall. (corrected on both the 2 disc Infinifilm DVD and the US Blu-Ray release of the film)
(at around 40 mins) When Nancy runs up the stairs near the end of the movie, the camera shows a close up of her feet sinking into the "goo" stairs. You can see exactly where she is going to put her feet as the "goo" pots are clearly visible.
(at around 1h 22 mins) After bringing Freddy into the real world, Nancy runs down to the front door and breaks the window. You can already see the cracks in the window that were probably made so it would break easier.