The house that Billy and Max's parents pull up to is not the same house that Lucas picked Max up from in the prior episode. When Lucas picked Max up, the front steps pointed toward the street and Billy was parked in the road in front of the house. When the parents return, they pull into a driveway that was not there earlier, the front steps are perpendicular to the road, and Billy's car is parked in the driveway.
When the team splits up (one team to deal with Will's condition and the other with the issue at the lab) you see Will is unconscious prior to everyone leaving the Byers house. In a following scene we see Jonathan and Joyce leaving in the car, as they pull away you can make out Will looking around in the back seat, wide awake. Nobody else goes with them in the car, so it must be Will.
The burial for Barb took place sometime in November or very early December, yet the trees in the background were still full of green leaves. Leaves in Indiana generally start turning color in late September or early October.
Chief Hopper has acquired an M4 carbine from the Department of Energy. While the M4 carbine had been in development since the early 80s, it would not be available to law enforcement and military until the late 1990's and early 2000's. The then-current AR-15 model available to government agencies would be the M16A1 or M16A2 rifles, or their lightweight short barrel counterparts the CAR-15.
The birth certificate that Dr. Owens gives to Hopper at the end of the episode is a modern Indiana birth certificate. Birth certificates from the 1980s did not have a blue border around the edges and the font was different.