When Zack and Kelly are discussing the periodic table, one shot has Zack holding a quarter of a banana. The camera switches to Kelly and when it switches back to Zack he is holding a fresh, unpeeled banana.
Alex models a red dress in her dorm room to wear at her job as a waitress. However, when she's working she wears a black dress.
It is clearly not 5 in the morning when Mike, Zack, Slater, and Screech go to the football field to practice - it's too bright. Even on the summer solstice, the longest day of the year, the sun would not rise until after 5 in the morning, and it would be some time after that before it became as bright out as it is in the training montage.
Zack and Slater both refer to Mike by his real name, "Bob," during a football practice montage.
Kelly says there are 103 elements. At the time this episode was filmed in 1993, there were 112 known elements.