The amount of makeup on Missy's face changes between shots.
The "People's Court" episode goes from introduction of the plaintiffs to the judgment in 20 seconds. Impossible.
Sheldon pronounces "et cetera" as "ek cetera". Sheldon knows his Latin and would know better.
Sheldon confronts the bully, Jason (Forrest Deal), with a small stone and a lab safety mask with a rubber headband, referencing David and Goliath, as he sets the stone and prepares to pull back the headband as if it were a slingshot. Anyone familiar with a slingshot would know that it needs an open space between the points where the sling is attached, which is why slingshots are always shaped like a "Y". The trajectory of the stone, once released, would be along a plane described by the point of the stone's release and the two points where the sling is attached. Sheldon surely would know that the physics of his situation would result in his stone hitting the lab safety mask and probably dropping somewhere near his feet.