During several of the nighttime searches, characters use flashlights with modern bulbs (identifiable by their blue-white color and visibly different from the yellow-orange hue of period-correct flashlights). Ironically, if they had all used modern bulbs, the error wouldn't be nearly so obvious.
The teenage characters frequently use the phrase "chill" to mean hang around. In 1983, "chill" would have been used as a command to someone the speaker perceived to be overexcited about something. "Chill" didn't mean "hang out" until some point in the 1990's.
When laboratory workers use hazard suits, there's clearly bright blue or white LEDs lighting up the face of the wearer. However, white LEDs were possible only since 1994 when Shuji Nakamura discovered high brightness blue LED, which emit white light when covered in phosphor coating.
The radio used by Chief Hopper was either a Motorola HT1000 or MT2000 series. Both came out around the late 90's. To be period accurate they would have used a model like MT1000.
In the early 1980s, the lights on the kids' bicycles would have been powered by a tire-driven dynamo. The dynamo's output and thus the light level would have varied according to the bike's speed, becoming totally dark when the bike was stopped.
Additionally, as with the "flashlights" anachronism, the headlights would have been yellowish, not the blue-white of a modern LED headlamp.
The story line predates many of the vehicles. The police chief drives a K5 Blazer with a facelift package which didn't come out until the next year, the buses all appear to be from the 90s - especially the bus on the International chassis near the end of Episode 8, which clearly has the 90s/2000s "anteater" style hood.
The police light-bar on the Chief Hopper's 1980 Blazer is a Code 3 MX7000, manufactured by Public Safety Equipment, which was not sold until the mid-1990's.
A number of times you can see the bad guys using Crosman 2240 airguns but they were not introduced until 1999.
While the HK MP-5K submachinegun carried by the Chief and the MPs/bad men existed as early as 1976 several characters are seen carrying MP-5K PDWs (identified by an attached sidefolding stock) which was not introduced until 1991.
Eleven is unfamiliar with the word "friend" until Mike tells her what it means. When she is being led to the Sensory Deprivation Chamber by Dr Brenner, he tells her that all the scientists are "friends"
In season 2, There are at least two different versions of Billy's blue Camaro used for filming as the vehicle will randomly switch from having power windows (as seen in S2:E2) to having manual crank style windows (as seen in S2:E5).
At the end of chapter 6 Mike and Dustin set their bikes down outside of Mikes house with Dustin's bike on the left and Mike's on the right. In the beginning of chapter 7 when they are leaving Mike's house to escape, Dustin's bike is now on the right and Mike's is on the left.
During a number of episodes, people are seen 'interrupting' someone talking on a two way radio or CB - that is, one person is talking/transmitting, and another person transmits to interrupt them, and then the other person hears this interruption and stops transmitting. This was done a few times on the kid's CB radios, and on the radios used by the police. Those radios - the CB and the police radios of the era from the show - don't work like that. If you are transmitting, and someone else transmits, you will not hear them.
The US flag patches worn by the police officers are incorrect. On the patches, the field of stars has too many stripes to the right of it and not enough stripes underneath. On the actual flag, the field "sits" on the fourth white stripe from the top. On the patches, it "sits" on the red stripe below it, the fifth red stripe.
CORRECTION: It's a myth that it's a "Federal offence" to impersonate a member of law enforcement by wearing an actual uniform in a movie or TV show. (It is a state offense to impersonate a police officer.) Accurate uniforms are allowed, but most production companies either don't bother to get them right, or don't work with the local LE agency and get their permission, and thus come up with something close but not quite right.
Indiana license plates should display a single digit or double digit at the begging on the number followed by a smaller letter and then up to four numbers after. The first digit(s) identify the county. So a plate would not start with 3X.