The amount of the Slurpee stain on Sheldon's shirt changes between shots.
When Mary is talking to Dr. John Sturgis, the position of the dial on her wristwatch changes between shots.
This episode takes place in 1991, but at the barbecue Mary attends, the song "Two Princes" by The Spin Doctors is playing and was released in 1992.
Even though Sheldon is a freshman college student he is never shown dealing with the basic core courses like English, history, government, biology, literature, etc.