Sheldon says to Amy that "Einstein failed math". This a false myth, originated by a 1935 article published in the "Ripley's Believe It or Not" magazine and very well alive to this day.
When Sheldon is shown looking down a microscope counting bacterial spores he is looking down the secondary viewing position and the a petri dish is on the bench. The petri dish should be on the microscope stage under the primary viewing position.
Sheldon mentions that he bought a Tamagotchi in 1998 and it was still alive. This would not be possible. When the battery dies the Tamagotchi resets. If you change the battery before it runs out the Tamagotchi resets.
There is a Caution Biohazard sign on the door of Amy's laboratory, clearly visible when Sheldon knocks on it. However, the door is propped open, highly unlikely if there are dangerous biological organisms inside.
While helping Amy in her lab, Sheldon defends himself against Amy's sarcasm by claiming that physicists like himself work with particles so small, they make 'fat jokes' about the brain slices that Amy notes are the width of a human hair. Sheldon decides to give an example of one of those 'fat jokes', when he says, "i.e., 'When your locus coeruleus sits around the house, it sits AROUND THE HOUSE.' Sheldon misuses the Latinism "i.e." (id est), which means "that is", and is used for re-stating something in different words. He should have used "e.g." (exempli gratia), which means "for the sake of example".
Amy instructs Sheldon to wash a tray of "beakers," but in fact only one of the items on the tray is actually a beaker: a straight-sided container with fully open top. The rest are all flasks: a container with a larger bottom part and a narrower neck and opening at the top.