When Max tries to run away & gets pulled back along the floor by Vecna, her hair changes from pony tail with scrunchy to without.
When escaping the Kamchatkan prison on a snowmobile, Hopper is shown with bare head, hands and feet. With temperatures far below freezing point and wind, body heat loss would be tremendous and death by hypothermia would occur quickly, or at least extremely severe frostbites leading to necrosis of various body parts.
Murray and Joyce drink roughly the same amount of drugged coffee at the same time, and Murray is unconscious first. Joyce would be unconscious first, since she has less body mass.
Dr. Owens takes Eleven to an abandoned ICBM silo in Nevada. Nevada is not a state that has (or had) ICBM silos.
During the shootout in the Byers residence one of the soldiers can be seen with a H&K G3 Assault Rifle. The only unit in the US armed forces to use this rifle during the Eighties were Navy Seals. The soldiers belong to the US Army, and would not have access to this weapon.
The "Yuri's Fish N' Fly" sign uses Comic Sans, which wasn't created until 1994.