Basic Crisis Room Decorum - S6-E3
Corrected entry: When we see the Dean's phone contacts, they're suppose to be in alphabetical order, but "Aisha" comes after "Andres" and before "Annie." It should be before "Andres." And "Albino?" is after "Freckles."
Corrected entry: It doesn't make any sense that the Dean would simply replace Chang with an actual Spanish teacher. It's ridiculous to assume that they would have learned what they should have with a fake teacher, even if he was convincing. What really should have happened was what happened at the end of Season 3, where their credit was annulled and they'd have to retake the course.
Correction: This is not a plot hole. The dean hired a new Spanish teacher to assess if the class has sufficient knowledge to pass, hence the test they take. The only reason they really passed is because it is implied Pierce seduced her. Any school would at least attempt to get the students through the year without failing their language, or it would look even worse on the school.
Pascal's Triangle Revisited - S1-E25
Corrected entry: When the Dean is telling Jeff and Annie about the dance, you can see that the buttons on his shirt are already undone so he can more easily pull it open to show Jeff his 'all 5 dances' t-shirt underneath.
Correction: That was his intention all along. He adores Jeff and always wants to either touch or impress him, so it's nothing out of the ordinary for his character.
Corrected entry: During several of the episodes, the cuts in the table from when Jeff hit it with an axe are seen. But during the credits sequence of the first episode, we Annie plastering the holes. So how did they get back?
Correction: All she did was fill in the holes to make the surface even. So there are still visible marks where the table was hit with the ax. The only way to make them go away entirely would be to paint the whole table, which we never see them do.
A Fistful of Paintballs - S2-E23
Corrected entry: When Annie comes in and shoots the cheerleader squad, there are six cheerleaders in the squad. One of them starts bickering with Annie and Annie shoots her again in response. But if her gun only held 6 bullets, and she shot all of the other cheerleaders, where did the seventh come from? And she never picked up another gun or reloaded after she shot them.
Correction: She only shoots 5 cheerleaders (you can count the shots and also see the paintballs hit). Annie leaves the middle, head cheerleader, unshot so she could have her "revenge" to her face. You see that before Annie shoots, the head cheerleader doesn't have paint. Annie only shoots her once (her 6th bullet), she never reshoots her or fired a 7th shot.
Debate 109 - S1-E9
Corrected entry: During the first debate, you can see the Human Being mascot in the bottom right side of the screen. When Jeff and Annie are walking out of the gym though, the Human Being is walking towards the gym. (00:09:15 - 00:10:05)
Correction: The last time we see the mascot is when they're announcing the scores. After that, the basketball team comes in and the debate is postponed. After that it cuts to Jeff and Annie walking out of the gym. However, the mascot is not walking towards the gym, he's walking down the hallway. Not only did he have plenty of time to get there, he could have simply walked out of the gym from a different exit and was heading in the opposite direction, as many other students were.
Advanced Advanced Dungeons & Dragons - S5-E10
Corrected entry: When Shirley finds out her character is a druid, she crosses herself, however, she crosses from right to left, the Orthodox cross, as opposed to the Catholic cross from left to right. Either way, Shirley is established as a Baptist, and they don't make the Sign of the Cross. (00:03:00)
Correction: As you pointed out, Shirley is Baptist and isn't aware how Orthodoxes make the sign of the cross. However, her established religion has no bearing on her making the sign of the cross, nor is it against her religion to make the sign.
A Fistful of Paintballs - S2-E23
Corrected entry: When the group arrives at Fort Hawthorne, Starburns tells them they need to give up their weapons, and Troy dumps his in the box. Then, Pierce tells Jeff that only "Hawthorne personnel" can carry weapons inside. Troy was a deputy, so he shouldn't have given his guns up (Starburns should also likely have said something to this). Troy may act silly sometimes, but there wasn't any bit here, so it's inconsistent with his character.
Correction: While he may have been working for Pierce, it is still highly unlikely he would let any member of the study group carry a weapon inside Fort Hawthorne. He was still angry at them for excluding him and wanted revenge.
Corrected entry: During Jeff and the coach's pool game, Jeff starts off sinking bigs, then switches to smalls, then back to bigs throughout the game.
Correction: On the break a striped ("bigs") ball goes in, however we see Jeff shoot solids throughout the rest of the game. It is the coach who is shooting the striped balls, not Jeff.
Early 21st Century Romanticism - S2-E15
Corrected entry: Duncan and Jeff meet at 6.30 p.m. to watch a soccer match between Liverpool and Manchester United. The time difference between the United States and England is at least 5 hours. Thus the game would have to be played in the middle of the night, which is inconceivable. (00:04:20)
Correction: It is never stated the game is live, it may well be time-delayed by the channel or recorded by John Duncan so that they can watch it in the evening.
Corrected entry: Pierce tells the Biology teacher that the study group members are the only people he has told about having sex with Eartha Kitt in an airplane bathroom. However, in 3.04 'Remedial Chaos Theory', Pierce tells the group about Eartha Kitt for the first time. Also, in 3.03 Shirley calls Britta's lighter her "marijuana lighter", but she doesn't find out about Britta smoking weed until 3.04. These errors are due to 3.03 and 3.04 being aired out of order according to their production, and have been acknowledged and confirmed by creator Dan Harmon himself, but they still count as mistakes.
Correction: Those two revelations only happened in the alternate timelines, not in the main timeline. In the main timeline, Pierce was about to mention Eartha Kitt, but was stopped (all he said was, "Airplane bathroom..." and was cut off), and Britta's smoking was never seen. Additionally, in the alternate timelines, nobody says or implies that it's their first time hearing about Earth Kitt (in fact, in one of them (the Darkest Timeline), they imply that they HAVE heard the story before, because Pierce mentions Eartha Kitt but not sex or the airplane, and the group is still disgusted) And Shirley was ranting about Britta's drug use which can very well be attributed to learning that the whole group decided not to eat her baked goods. It can only be assumed that the revelations came some time before episode 3, off screen. The mention of them being shown out of order is irrelevant given these facts.
Corrected entry: In the final scene, when the camera pans from Vaughn's group to follow Jeff, the statue of Luis Guzman can be seen in the background, despite not being revealed until the following episode.
Correction: The statue existed at that point in time. The absence of a cover on it does not make it a mistake.
Corrected entry: It's obvious that the coach is strict about wearing the P.E. uniform in class, but when Jeff agrees to play pool in shorts, none of the students the coach is playing pool with behind him are wearing the uniform.
Correction: The scene doesn't take place in gym class. In the P.E. Room, the pool table has a red felt, this one they play on has a green felt. They're at a student lounge (with tables, stools, and vending machines) outside of class.
Correction: On many phones you can reorder contacts to match the frequency with which you contact them.