When Jeff and Pierce begin studying, Jeff empties his glass and places it on the table. When the angle changes, his glass still has liquid in it.
When Pierce is pouring whiskey, the scene cuts between him filling the first and second glass, with no pause in the sound of the whiskey filling the glasses, even though the glasses are too far apart to fill in one motion.
After using the Silly String in their presentation, Jeff's sweater is absolutely covered in Silly String (which is wet and messy) but when he exits the classroom the front of his sweater is pristine and only his shoulders have a trace of where Silly String used to be. They'd never be able to wipe it off completely - and in such a short amount of time - not to mention the fact that Silly String stains clothing.
When Pierce comes out to berate Jeff while he is at the protest with Britta, Jeff lowers the sign he is holding and turns to face Pierce. In the next shot, from behind Jeff, as Pierce continues to approach him, he is holding the sign up again and immediately lowers it.
At the end, when Troy and Abed are rapping in Spanish at some point they say "nieve" which means "snow", however on the screen the English translation is "ice cream".
At 09:06 -there is no tax stamp on the liquor bottle which makes possession and consumption both felonies.