While commandeering Todd's car, Hopper gives Todd his pepperoni stick. After Joyce joins them, Hopper has the pepperoni stick and again, gives it to Todd.
When Grigori finds Hopper's truck in the woods, black smoke is billowing from the passenger side. When he starts to walk away and the camera switches to a wider angle, the smoke is all but gone.
The candy poured out of the brown (plain) M&M bag appear to be Skittles. The candies are too fat for plain M&Ms and the colors match those of Skittles and not era-appropriate M&Ms.
When Murray (Brett Gelman) opens the door and points the shotgun at Joyce (Winona Ryder) and Hopper (David Harbour) it makes a sliding cock sound. This is a fixed single shot double barrel weapon. It has no slide or cocking feature at all. Designed for duck hunting, it wouldn't make a sound.
The shotgun Murry uses is a double barrel rifle used in skeet shooting. It doesn't make any slide cocking sound. This sound incorrect, it's from a normal repeating shotgun.
At 23:27 Cigarettes can be seen on display behind the cashier at the 7 Eleven. Just beneath the Winston sign to the left of the display are non-menthol Newport cigarettes for sale in red and yellow packs. However, this would not be possible considering that the show is set in the late 1980's and Newport didn't first try selling non-menthols until the mid 1990's.
When Hopper's Chevy Blazer breaks down in the woods and Joyce is talking to Alexei, the Russian is clearly handcuffed around a tree. When the scene cuts to a side-shot, it looks like the tree is gone and Alexei is not handcuffed to anything, but it's because of the position of the camera and the framing; the tree is still visible behind Alexei's head.
When Murray Bauman (Brett Gelman) pulls his shotgun on Alexi (Alec Utgoff), it makes the familiar cocking noise of a pump action shotgun. However, he's using a side by side double barrel shotgun which doesn't have this.
At around 00:38, Steve (Joe Keery) says "Get this off of me!" but his mouth does not move. His hand briefly covers his face however it is still visible that he is not speaking.
While trying to escape the Russian facility, Dustin and his group look at the strange machine and the men working on it through some glass panes on a door. When the camera pans out, one of the scientists strolling through the room stops near a desk and looks directly at the door and the kids, not reacting at all.
When Mike pours some of his M&M's into El's hand, you can see one of the M&M's is red, however, red M&M's were discontinued between 1976 and 1987 due to concerns that some red dyes were a health risk.
When Hopper commandeers the car at the gas station, the fuel nozzle is the vapor recovery type. Vapor Recovery nozzles weren't in use in the US at that time, except for California.
The Russian underground complex should have guards in the long tunnel entrance, but when the kids enter it does not.
When entering the facility, Chief Hopper shoots the card lock on the opposite side of the door from the outside in an attempt to prevent pursuit. Because the card lock on the outside is undamaged, shooting the card lock on the inside should do nothing except hinder escape.