When the Mind Flayer's ooze descended into the sewers, a large bone was too large to fit through the sewer grate. However, just prior when the ooze flowed through the hospital door's lower vent & under the door, the same bone wouldn't have fit through those narrow gaps either.
When Eleven is looking for the source inside Billy's memory, the blood from her nose keeps changing from wet to dry.
El has manicured fingernails at one point during her vision of Billy's childhood. She never has manicured nails at any other time.
In one scene, Mayor Kline got beaten up and was wearing sunglasses to hide a swollen eye. In the next scene, at the 4th July fireworks, the bruising is gone.
When El finds the source in the abandoned steel mill, Jonathan looks up the location in the Yellow Pages. If the building has been abandoned for some time, the location and number would no longer be listed in the phone book.
Dustin tells Erica that one way he knows she's a nerd is because she likes My Little Pony, but My Little Pony 'n Friends didn't start until 1986.
The "Mayor Kline Presents" banner features the font Gotham Serif, which wasn't created until 2011, and Gotham, created 2004.
The "Total" logo seen in the oil drums outside Murray's bunker is not the one used in the 1980's, but the one introduced in 2003 (still in use nowadays).
When the Russian interrogator wags his finger at Robin, his mouth visibly moves, but no sound comes out.
Robin's words don't always match her mouth, in the scene where she is reunited with Steve. For example, one time she says, "Steve!" her lips don't move at all.
It does not make any sense for the Russians to transmit the radio message. Its sole purpose is so the protagonists can uncover the secret installation under the mall.
Hawkins Memorial Hospital is so woefully understaffed that none of the many strange happenings even get noticed by the hospital personnel.
There is no explanation provided as to how the Russians managed to construct a massive underground tunnel complex (accessible only by an extremely deep shaft) directly below a mall located in Indiana without notice.