During a flashback, Dr. Brenner tells Eleven not to be afraid of the scientists and lab technicians, and that they are all friends. In an earlier scene (but later chronologically) the boys say the word "friend" to Eleven and she doesn't know its meaning and it needs to be defined, yet she's heard it before.
In the first episode, the Dustin makes a reference to Nancy dressing up for one of their campaigns four years ago. When Dustin and Mike are discussing best friends, Dustin alludes to the fact that they didn't meet until the fourth grade. Since it's apparent that the boys are in seventh grade, Dustin and Mike only met three years ago and therefore he shouldn't have firsthand knowledge of this.
When Eleven is looking at her mirror image in the lake, the morning light is illuminating the right side of her face, but the mirror image in the lake is being illuminated from her right as well. As a mirror image, her mirrored face should have been illuminated from the left.
While Eleven gets lowered into the tank, the socket of the EEG is dangling on the backside. However in the next shot it's in front on her right side.
In an episode 5 flashback Will is shown finishing a drawing of his Dungeons and Dragons character by adding green fireballs; in episode 6 Joyce shows what is supposed to be the same drawing to Hopper, but the fireballs are now a different shape and depicted in a straight line rather than in a cluster as they were previously.
When Eleven gets prepared for the tank, an EEG sensor net is placed on her head. However it is not connected, the empty socket is dangling visibly from the back of her head. It can't be a radio transmitter either since this would interfere with the sensors.
When Nancy and John are shopping for "monster hunting" supplies, John asks the clerk for four boxes of .38's. The Smith and Wesson Model 10 that they have, shoots .38 special. The ammo that they purchase are .38 super auto and would not work in their gun.
While in the surplus store, Jonathan and Nancy request boxes of .38 ammunition, but the boxes the clerk puts on the counter read .38 Super Auto; a completely different cartridge from the .38 Special revolver taken from his father's car.
Before Eleven looks in the pond, the shadows are on the left side of her face, but in the "reflection", the shadows are on the right side of her face.
During the supermarket scene, Eleven can be seen walking past a pack of Trident White gum. Trident White wasn't introduced until 2001.
When Eleven first walks into the supermarket, two modern cars pass by in the distance.
The MP's at the Lab are all carrying Beretta 92F pistols. The US Army was still using the Colt 1911 .45 cal. pistol in 1983. The Beretta was not adopted until 1985.
After the cold open, "Sunglasses at Night" is playing as Steve and his friends drive in his car. The song was released in January 1984 as an official single, and was not popular until later that year, reaching its peak in August. "Stranger Things" takes place in November 1983.
When Nancy and Jonathan are in the army surplus store, Nancy picks up a mallet and then sets it back down with a metallic clang before selecting another. But the first mallet has a rubber head and a wooden handle, so it wouldn't make that type of sound.
When Joyce and Hopper take off from the phone booth, the road has reflective plastic bumps down the center line. These are not used in northern climes (like Indiana) where it snows, as they interfere with snowplows.