Hopper and Joyce are dressed in protective suits because the atmosphere in the Upside Down is toxic. Yet Nancy didn't seem to be affected by it when she entered the Upside Down via the tree portal.
Jonathan's '71 Ford Ltd has a brake light out (driver's side) at the end of Ch. 7. By evening of the same day, now Ch. 8, both brake lights work.
At around 33:30, when Eleven is laying on the table, you can see her dress under her rolled up sleeve. When the camera switches to Mike's point of view, the sleeve is no longer rolled up and the dress can't be seen.
In Hopper's flashback, the doctors are performing CPR on his intubated daughter while the ECG monitor is beeping, meaning it still detects a heartbeat. It's only a few seconds later that the ECG flatlines, meaning there's no electrical activity detected in the heart. CPR is performed in an effort to restart that electrical activity, meaning it should have been started after the ECG flatlined and certainly not before.
When Hopper is performing CPR on Will, it is in the modern 30 compression and 2 breaths (30:2). In the 1980's the standard ratio was 15:3. The change to 30:2 came in 2005.
When the Blazer is pulling off the road into the snow, you can see tire tracks in the snow from previous takes.
In the article "Hawkins lab blocks inquiry" posted on the cork board in the police station at the end, the second and third paragraph have the exact same text in them.
When Nancy, Steve and Jonathan are running away from the monster in Jonathan's house, they jump over the traps they set in the corridor. Problem is that those traps weren't added to the final montage in post-processing so they jump over nothing.
When Hopper is making his deal with Brenner, he insists that they "leave those other three kids, those boys, alone". When he left, Nancy and Johnathan were still there, so he should be insisting that they leave all five of them alone. He has no way of knowing that Nancy and Johnathan are no longer there.
In "The Upside Down" the form of CPR used by Chief Hopper is actually the latest method of CPR (30 compressions:2 breaths) introduced in the 2010's. The way CPR was performed in 1983 was 5 compressions:1 breath.
The yellow bio suits that are used by both Nancy and Hopper and previously by a military personnel clearly have LED lights in the helmet used to illuminate their face. LED lights with that color and brightness were not available in the 1980's.
Some of the MP's entering the school are carrying MP5 PDW's, which weren't introduced until 1991.
The periodic table in the science classroom has several chemical elements which had not been discovered or named in 1983. For example, Livermorium (Lv) was discovered in 2000 and wasn't named until 2012.
Near the end, the boys get into a car and buckle up. Seat belt laws were enacted in 1984. Practically no one buckled up back then, until it became law.
At 26:51 -one soldier says "sir, we've searched everywhere; there's no sign of them" while standing beside the wading pool and supplies left there in the gymnasium by the "fugitives".