Continuity mistake: You can see the play director telling a pianist with grey hair to "play something modern." About twenty seconds later when Britta throws her tea hat off towards the pianist, however, it's an entirely different piano player now, that has brown/black hair. (00:17:10)
Continuity mistake: After the pottery class scene, in the Spanish classroom, when Britta and Jeff are talking, his right arm is across the desk. When Jeff replies "so did someone's psych teacher" and camera cuts, his arm is suddenly folded up by his chest. In the next shot, his left hand is suddenly over his right hand.
Revealing mistake: When Chang's paint bomb explodes, pay attention to the background. You will see paint exploding from three different points on the ground. (One to the center, one to the left and one to the right) The only problem is that there was only one paint bomb in the center, so it makes no sense that there are 3 explosions from different points.
Continuity mistake: The study-room on the second floor of the library, right next to a set of stairs, and the area isn't particularly bright. In the rest of the series, the study room (which is meant to be the same study-room) is now located on the first floor of the library, nowhere near any visible stairs and the area is much brighter and more well-lit. As often happens, the pilot was filmed before any other episode, and the setting was changed in the meantime.
Continuity mistake: At the end when Abed is talking to the Dean, there's an open to-go box with chicken fingers. After the Dean asks who would steal a box of hairnets, it cuts back to Abed and the box and ketchup are gone. Post-it notes are also now seen and the stapler moved. In the next shot of Abed, the chicken is back.
Continuity mistake: In the very first shot, we can see there's a man with a dark coat, sunglasses, short hair and earbuds standing directly in front of the dean. When it cuts to the opposite angle, he's no longer there. When it cuts back to the first angle a few shots later, he's suddenly back.
Continuity mistake: When Jeff and Pierce are having a glass of whiskey, Pierce makes a toast and Jeff replies "To the irony of that sentence." After he says this, Jeff puts his glass back on the table and Pierce lowers his glass, but doesn't put it back on the table. In the next shot, Pierce's glass is suddenly on the table. (00:09:35)