When Eleven and Jim are having a conversation at the table, one camera angle appears to show Eleven sitting back in her chair while Jim is talking, then suddenly another camera angle shows Eleven leaning with her elbows on the table. This interchanges a few notable times during their conversation.
When Billy drives the car recklessly with Max in the passenger seat, there is a panned shot of the water tower, car park and Max on her skateboard. The water tower has digital cellular transceiver antennae around it. Digital cellular networks were not invented until at least 20 years later.
The cold open takes place at the end of the previous season (1983), a year prior to this season. Finn Wolfhard has noticeably matured between taping the first season and the second season so he looks different during his interview with the "Fed".
In the flashbacks of what happened to Eleven between killing the Demogorgon and living with Hopper, her hair has grown significantly. This is particularly noticeable when the hunter approaches her at the campfire.
The digital watch Dustin wears is a Casio F-91W. While 80s in style, these were only produced from 1991 and are still available today.
A 1993 version of "Monster Mash" by Bobby "Boris" Pickett can be playing while the Party goes trick-or-treating. It hasn't been out in 1984.
When Lucas and Dustin first approach Max to talk to her, she identifies the Ghsotbuster packs as "Proton packs." They weren't called that until the cartoon a couple of years later, just accelerators.
From 16:04 -it is highly unlikely that the major electric service to such a large complex would be inside a ruined shack located out in the middle of nowhere.
In one scene, the boys dress up as Ghostbusters and were looking at the bus. One girl is walking to the school. In another scene, the girl is walking out of the bus.
In one scene, the boys dress like Ghostbusters, two girls were shown carrying lunchboxes walking. In another scene, the two girls were holding hands. In the scene where Dustin and Lucas were looking at Max, the two girls were together, except they weren't holding hands.