In the flashback to Cooperative Calligraphy (2010), students are seen waiting outside the Study Room while the group searched each other in their underwear. However, according to Dean Pelton's announcement just a minute later, everybody was on the quad at the puppy parade at that moment.
In the flashback to Advanced Dungeons & Dragons (2011), Jeff's outfit is similar to one he wore in the episode but is noticeably colored differently. Also, Leonard is seen trying to get into Group Study Room F's closed doors, but the doors were never closed in this episode. In addition, the flashback shows many students in the background. The D&D game was held on a Saturday, when there would be few (if any) students. None were shown in the background in the D&D episode.
When Troy pops out of the oversized cake, the hard round lid falls to the floor behind him. In the next shot there is a flexible lid draped over the side of the cake.