In the very beginning, when Hopper is in Joyce's house, the lights from the police cars are seen flashing into the house, even as Hopper turns around to leave. When Hopper walks out of the house, there are no flashing lights.
As the boys carry away Eleven, it can clearly be seen at 41:51 that there is no fire damage or fire extinguisher residue left behind on any of the equipment that had caught on fire.
When the kids are taking unconscious El out of the Heathkit room, her right sleeve is slightly up, allowing for her watch to be seen. In the next shot, before anyone could have moved her sleeve, the watch is not visible.
When the scientist, Sheppard, is exploring the upside down while tethered to where the other scientists are back at the lab, he tells them that he's traveled about a click (one kilometer) from the tear. The viewer can then see that very little of the cable is missing from the reel. He then encounters the monster and radios for them to reel him back in. At the speed he is reeled back in, no more than a couple hundred feet of cable (well short of a kilometer) is reeled in before the bloody harness appears.
The hole in the wall made with the axe is in no way as large on the inside as it is on the outside; however, when the camera pans out, the hole is big enough for the viewer to see Joyce's whole face. Furthermore, although the hole was made from the inside, there is no debris at all outside.
In addition to the flag for the state of Georgia being visible, it is the current (2016) flag, not the flag in use in 1983.
One of the military personnel guarding the government lab facility is carrying what appears to be an M9 pistol (a Beretta 92FS built to military specifications). The show is set in 1983, and the US military did not begin adopting the M9 until 1985, with the M9 fully entering service in 1990.
When the boys are riding the bikes through town, there is a shot facing the three of them and there is a current day vehicle parked in the background.
When Mike tries to convince the group that Will is alive it appears that 2 shots are in the wrong order, as the first where Mike says "he's out there somewhere" his mouth is clearly not moving and a few shots later you can see his mouth moving with no sound.
At 47:33- boom mic visible far-right by the bird bath.