Many series throughout television history have had the misfortune of suffering setbacks during the show's run, and Community was no different, stumbling over a few bumps in the road when the series creator, Dan Harmon, was fired after season 3, resulting in a season 4 that is generally ridiculed among the series' loyal fans.
Luckily, the show realized its error and brought Harmon back, allowing the show to return to its roots and get back to what it was really all about in the first place - a group of misfits attending a community college.
G.I. Jeff, Episode 11 (8.0)
One of the show's main themes of the show was that the characters (especially Abed) were aware of how meta they were. It couldn't have been displayed any better than during this episode, done in the same style as the 80's cartoon G.I. Joe. Things immediately start off rocky when Jeff's character (Wingman) kills a member of Cobra (something that has never occurred). As the episode carries on, it's revealed that the entire premise is happening inside of Jeff's head while he lays comatose in a hospital bed.
Analysis of Cork-Based Networking, Episode 6 (8.1)
Annie got a bitter taste of what it costs to get things done during this episode, as the entire premise centers around her trying to get authorization to put up a new cork-board in the cafeteria. Annie ends up having to jump through numerous hoops and owes so many favors that by the time she gets the proper authorization, the decisions she's made in order to make it happen have rendered the cork-board worthless. Meanwhile, the rest of the Save Greendale Committee is tasked with organizing a school-dance, which (thanks to Chang) turns into a total catastrophe.
VCR Maintenance and Educational Publishing, Episode 9 (8.1)
When Jeff, Shirley, and Hickey discover a locker full of untouched Chemistry textbooks (worth over $100 each), the three of them decide to sell the missing merchandise and pocket the profits. However, upon setting up a meeting with a buyer, the buyer points out the obvious flaw that every textbook is missing page numbers, making them worthless.
Meanwhile, Abed and Annie (missing Troy) use a low-tech interactive VCR game to fight over who will become their new third roommate. However, due to their aggressiveness, they drive both of their candidates (Abed's girlfriend and Annie's brother) away.
Basic Sandwich, Episode 13 (8.2)
The season 5 finale dealt with the aftermath of the prior episode (Greendale being sold to Subway) and led to the Save Greendale Committee on a treasure hunt into a secret trap-door underneath the school. Inside, the Committee finds the original owner of Greendale, disgusting but still alive, as well as a giant sack of money that they can use to buy the school. However, it turns out not to be necessary, as Jeff discovers a loophole stating that the original owner (whom they found in the trap-door) will be partners with Subway upon completion of sale. After taking one look at the man, Subway backs out of their contract and the Save Greendale Committee pulls through one last time.
Introduction to Teaching, Episode 2 (8.5)
All of the main characters graduated at the end of season 4. So, what were the writers to do? Bring everyone back, of course! However, Jeff didn't come back as a student like the rest of the group - he came back as a professor of law. While helping the Dean save the school, Jeff is forced to become a professor in order to pay the bills, but of course, he slacks off. This causes Annie to throw a fit and try and force him to become a better teacher (which, somehow, manages to work).
Advanced Advanced Dungeons & Dragons, Episode 10 (8.5)
After their game of Dungeons & Dragons successfully got Neil out of his funk in season 2, the gang only deemed it fitting that another game of D&D would help bring Hickey and his estranged son closer together. However, recognizing the ruse for what it is, Hickey's son purposely derails the game by getting the members of the quest separated... prompting Hickey to make a wager with his son over who wins the game. At the end of the episode, after everybody else's character has been killed, Hickey and his son are left alone to bicker back and forth about the game - which (Jeff points out) is the best some sons and fathers can ask for.
Basic Intergluteal Numismatics, Episode 3 (9.0)
This episode had everybody... cracking up. But seriously, things got a little too weird during this episode with the premise revolving around the infamous Ass-Crack Bandit, an anonymous member of the Greendale student body who slips quarters into people's butt-cracks when they bend over.
As Jeff and Annie try to discover the identity of the ACB, they end up uncovering the secret that Starburns (who had died in season 3) was actually still alive. Starburns confesses to being the ACB, but Jeff realizes he's lying and continues to follow the ACB's trail... only for the episode to abruptly end with the revelation that Pierce Hawthorne had died.
App Development and Condiments, Episode 8 (9.0)
Let's be honest - social media has gotten a tad out of hand, and Community felt the need to highlight that fact during this episode. It opens with an app development company using the Greendale student-body as guinea pigs for their new app, which essentially just rated humans on a scale of 1-5. As the episode goes on, students download the app, and everyone immediately gets categorized by what "number" they rank. The 5's start to take over society while the 1's are considered less-than peasants... eventually ending with everybody giving the app 1 star on the App Store and deleting it altogether.
Cooperative Polygraphy, Episode 4 (9.3)
As stated above, Pierce was pronounced dead at the end of episode 3, and it turned out that he left something to each member of the study group in his will. However, there's a catch - they only receive what they're due if they pass a polygraph test, orchestrated by Pierce himself. The episode then revolves around the members of the study group getting asked personal questions from Pierce's beneficiary, resulting in the group immediately turning on one another upon hearing the answers to said questions. After resolving their issues, passing the tests, and receiving their compensation... it's revealed that Troy will also be awarded $14.3 million if he sails around the world, forcing him to leave Greendale to undergo the journey.
Geothermal Escapism, Episode 5 (9.4)
Following the announcement that Troy would be leaving to sail around the world, it was only fitting that Abed give his best-friend a proper send-off... with a school-wide game of Hot Lava! A twist on the show's paintball staple, the episode follows the study-group as they all try to be the last person to touch the floor (and win a prize of $50,000). However, toward the end, the game is revealed to be "real" to Abed, meant to be a coping mechanism to deal with the reality of Troy leaving. Luckily, Troy and Britta are able to "clone" Abed and help him accept this new reality (due to being in his new clone body). The episode ends with Troy getting on a boat with Levar Burton and sailing off... into land-locked Colorado.