Other mistake: In the beginning when Kali and her gang are running from the police in Pittsburgh and she "collapses" the tunnel, her 008 tattoo is shown this way so we can read it as such, but it should in fact be read 800 to be the correct way. (00:03:15)
Factual error: During the police pursuit in Pittsburgh, the officers are wearing shoulder speaker/microphone handsets. The models are the Motorola Saber radio, which wasn't introduced until 1989, while the season takes place in 1984.
Revealing mistake: When Bob and Joyce have lunch, Bob pops open a can of soda (which is period appropriate). The scene cuts to Joyce, then back to Bob. It is clear from how he is holding the can, and how he pretends to drink from it, that his newly opened soda is actually empty.
Answer: The body was fake, made by the scientists at Hawkins Lab in an attempt to cover up his disappearance and the existence of the Upside Down.