In a scene set in 1959, Jeffrey Dahmer's mother states being 26 weeks pregnant. Jeffrey Dahmer was born May 21, 1960, making the date of his conception roughly August 27, 1959. 26 weeks from then would be late February, so it should've already been 1960.
When Joyce tells her doctor she is 26 weeks pregnant, he replies that she is well into her last trimester. However, the last trimester does not even begin until 27 weeks of pregnancy.
At around 11 minutes, there is one shot in which two periodic tables can be seen hanging on the walls of the science classroom where the class dissects a piglet. The one on the left shows 107 elements, the final one being Bohrium, discovered in 1976. The one on the right, however, shows 116 elements, going all the way up to Livermorium. However, Livermorium wasn't discovered until 2000, making that periodic table about 20 years too recent.
In scenes set in 1977/78, the songs Please Don't Go and Stumblin' In are heard. These were not released until 1979.
When Dahmer hears his parents arguing and leaves his room to investigate, it is shown that his door is a sliding door rather than a door with a hinge. However, when he returns to his room, the sound is clearly for a door swinging/slamming shut, which his sliding door cannot do.