Much of the humor from the animated series Family Guy comes from the characters failing to recognize their own stupidity, being clueless when others harshly criticize them and so forth.
In the Season 3 episode "To Love and Die in Dixie," the Griffins are placed in the Witness Protection Program after an armed robber threatens to kill the star witness Chris. Several examples abound: Early on: Peter is sent to the police station to pick up Chris, who is giving a statement after witnessing the robbery and is being asked to identify him in a police lineup. You'd expect: The receptionist to have Peter wait in the lobby until Chris comes out. Instead: Peter is somehow able to wander into police lineup room, where he shows someone he thinks is a police officer Chris' photo. The man turns out to be the suspect. Later, after the Griffins are sent to the South to live (after the robbery suspect escapes from jail): Two police agents are hired to stay at the Griffins' home until the armed robbery suspect is brought back into custody and is no longer deemed a threat. One evening, the robber visits the Griffins' home, hoping to find Chris and to carry out an earlier threat to kill him. However, when he initially asks the agents if Chris is home and they reply that he is not, the robber realizes his mistake and asks where Meg is living. You'd expect: The police officers to have the man arrested. At the very least, one would think they would be tipped off by the man's earlier slip that their visitor might harbor a sinister motive. Additionally, the two officers also had a description of the armed robber suspect and were aware from their (unseen) briefing that he was likely trying to find Chris. Instead: The addle-brained cops reveal where Chris is living. And finally: Herbert, the elderly pedophile who wants to consummate a sexual relationship with Chris. You'd expect: That with 113 messages left on the Griffins' voice mail, all from Herbert demanding to see or talk to Chris, that Peter and/or Lois would get suspicious about the caller and have the police charge Herbert for (at the very least) making harassing phone calls. Instead: They ignore it, setting up a series of encounters later on with Chris, who at least is able to if only unwittingly ward off his predator. (Peter and Lois seem to have no knowledge of Herbert's background, and indeed very little has been revealed about Herbert's past, except that he was in the Army Air Forces during World War II.)
In the Season 6 episode "McStroke," Stewie inspired by the teen dramas such as One Tree Hill decides to masquerade as a teenager named Zach Sawyer and enroll at James Woods High School. You'd expect: The school administration to ask "Zach" who his parents are, or perhaps contact his former school to obtain a transcript. Instead: No background check is done, and "Zach" is allowed to enroll. You'd expect: Connie D'Amico the self-described most popular girl at school to suspect that "Zach" is actually Stewie, since she has seen him several times and, knowing who he is, would suspect that the physical features of "Zach" strongly resemble 1 1/2-year-old Stewie. In the very least, she is aware that Meg has two brothers: Chris and Stewie. And, as Connie is an intelligent person, she is or should know that having a romantic relationship with a toddler is morally wrong and illegal, and that by asking someone she has a feeling might be too young for her out, she could risk being arrested, lifetime placement on the Sex Offender Registry, and ruined social standing. Instead: Connie asks "Zach" out, and when she tries to initiate sex, she finally realizes that he is a baby. Instead of realizing that she could be in very deep legal trouble, Connie still wanting to believe that "Zach" is actually a teenager arrogantly has him ostracized for his small, well, "thing." Stewie finally reveals himself, and just as quickly Connie is arrested for lascivious acts with a child.
In Season 6's "Back to the Woods," James Woods — wanting revenge for his arrest for stalking Peter (in the Season 5 episode "Peter's Got Woods") — steals Peter's identity, moves into his house and refuses to leave. When Peter objects, Woods calls the police to have Peter removed from the premises. Officer Joe Swanson shows up and upon questioning, Woods shows him documents that prove that he, not the real Peter, is Peter Griffin. You'd expect: That Joe, knowing Peter as his best friend for years, would arrest Woods for forgery and identity theft. Instead: Joe believes Woods instead, claiming the paperwork shown is legal. Lois calls Joe out for being such an idiot, but Joe decides to follow the "law" and boot Peter out of his own home, not even bothering to ask Peter to see HIS own forms of identification to at least prove that Woods is impersonating Peter. Later: After Peter's attempt to reunite with his family fails (Woods tricks the obviously disguised-as-Chris'-new-friend Peter into revealing his true identity), Peter and Brian decide that turnabout is fair play, and before long Peter assumes Woods' identity and books himself as a guest on Late Night With David Letterman. You'd expect: Letterman, knowing who Woods is, to immediately kick Peter-as-James Woods off the show and have security escort him from the studio. Instead: Peter successfully convinces Letterman that he is James Woods, then procedes to destroy Woods' reputation by making slanderous, inconsiderate remarks before the coup de grace: claiming that he is making a slapstick comedy short based on the 9/11 attacks. In the closing scene: Woods tracks Peter down to an alley, where he hopes to engage in a confrontation. Instead, he finds a trail of Reese's Pieces. You'd expect: Woods to immediately get wise, knowing that this is a trap (as he was caught in a similar booby trap a year earlier). Instead: "Ooh, a piece of candy! Ooh, a piece of candy! Ooh, a piece of candy! Ooh... " The box slams down on top of Woods, and Peter and Brian stand guard until the authorities arrive to take Woods into custody.
In the Season 4 episode "Patriot Games," Stewie has already beaten up Brian for holding out on the $50 he lost on a bet. Upstairs, he sees Stewie playing golf in the hallway so he puts on a mustache, hoping to sneak past him. You'd expect: Brian to keep his mouth shut if he doesn't want a repeat of what happened before or, better yet, just pay Stewie the $50. Instead: He greets Stewie who at first falls for the disguise but catches on immediately afterward. Stewie dishes out another ruthless beating, worse than before.
Season 8's "Family Goy" — an episode that mocked the Jewish faith — begins with Peter and his friends at the Drunken Clam, and proprieter Hoarce disposing of old life-sized cardboard cutouts in the trash bin. Peter sees one of the cutouts — that of Kathy Ireland — falls in love with it and, not wanting to see an inanimate object depicting the beautiful Ireland in a particularly physically attractive pose destroyed, asks to take it home, to which Hoarce consents. You'd expect: Peter to at least realize that the cutout is not a living object and keep it simply as a souvenir... if only to masturbate to when looking at it. (See next line for why.) Instead: He serenades "Kathy" with Billy Ocean's "Suddenly Last Summer" while at the bar, before later treating the item as his girlfriend, as though she were a living, breathing human being. (Examples include going for a ride in the country and simulating sex with it.) Later, when Chris takes the cutout into his room, Peter becomes very angry (because "Kathy betrayed" him) and strikes the cutout, causing its head to fall off, and he winds up burying it in his yard, somehow thinking he killed a human being and was trying to cover up his crime(!). Even better: When Lois sees Peter laying on top of the cutout and expresses her disgust, she points out Peter getting into a turf war with — of all things — a cat!!!!! Later: In a scene emulating an infamous sequence from Schindler's List, Peter, having become an anti-Semitic after his father — Francis, not the town drunk from Ireland as revealed in "Peter's Two Dads"— comes back from the dead to warn Peter that he'll end up in Hell for leaving the Catholic faith, shoots at his Jewish friend and neighbor, Mort Goldman, from his upstairs window while Mort is at his mailbox. You'd expect: Peter to be arrested almost immediately. Instead: Police officer Joe Swanson — another of Peter's neighbors — not only lets Peter get away with it, but he too (a policeman(!)) also shoots at Mort as his morning greeting. Mort resignedly says, in essence, this is par for the course.
In the Season 8 episode "Dial Meg for Murder," Meg has been sent to prison for harboring an escaped fugitive (whom she fell in love with). She returns with a hardened attitude, wanting revenge on her family and school mates who have taunted and/or abused her through the years. You'd expect: Connie and her friends to avoid her now that she's not the mousy, little nerd-girl she once was. Instead:They make fun of her as usual, and Meg finally beats up and humiliates Connie.
In the end of the same episode, Meg kidnaps Brian at gunpoint and takes him away in the car. She then pulls up to Goldman's Pharmacy, orders Brian to stay in the car, and attempts to rob the store. You'd expect: Brian to stay in the car or run somewhere else and call the police. Instead: Brian goes into the store, sees what Meg is doing, and threatens to call the cops if Meg doesn't put the gun away. Meg could have easily turned around and shot Brian (fortunately, she didn't).
Season 8's "Big Man on Hippocampus" saw the Griffins appear on Family Feud, where they win their way to Fast Money. Lois provides all the No. 1 answers and scores 199 points in the first half of the game, one point away from winning the $5,000 grand prize. Peter has been chosen to play the second half of the game. You'd expect: Peter to easily come up with at least one answer that will push the family's total above 200 and thus net them the $5,000 prize. Instead: On the first question — "Name something you sit in" — Peter duplicates Lois' answer, "chair." Not a problem, as the rules provided that a duplicated answer would be buzzed and the contestant would be prompted to give another answer. However, Peter insists on giving "chair" as his answer (trying "big chair" and "little chair") before insisting that he wants to be credited with "chair," wasting precious time. He then asks, "What if I can't think of anything else?" to which Dawson tells him he can pass the question. So now you'd expect: Peter to pass and hear the next question. Instead: At least another four seconds are wasted by him asking, "How do I pass?" to which Dawson gives the obvious answer (and to add to Peter's stupidity, he asks for a clarification(!)). Peter can only blurt out, "Chair." In the end, time expires, and (at least in fiction) the Griffins, thanks to Peter, are responsible for the biggest Fast Money meltdown in history.
Season 12's "Brian's a Bad Father" sees Peter engage in some highly criminal activity when he "blows a raspberry" to a 3-year-old girl in a private place. Joe (a police officer) and Quagmire himself sexually deviant witness the incident (which takes place off-screen). You'd expect: Peter to be arrested immediately, or in the very least beaten until he is nearly unconscious. Instead: While Joe and Quagmire indeed watch with horror and disbelief, they do nothing! All Joe says to Peter after seeing the whole thing is that maybe he should go home now and then he remains friends afterward, chalking it up as Peter the all-around good guy being just a little bit screwed in the head now and then.
In the episode "No Meals on Wheels," Peter opens up a restaurant and it doesn't do well at all until Joe and his friends stop by the place to eat, which makes the place become a huge hit. The only thing about it is everyone is handicapped, which bothers Peter greatly because it makes the place "less cool." You'd expect: Peter would just suck it up and accept the fact that his restaurant is making a ton of money and that it doesn't matter who comes to eat. Instead: Peter decides to make a new policy denying service to the handicapped because the restaurant is no longer cool by Peter's standards. In the end: Laser-Guided Karma slams Peter hard by having him become injured when Joe and his friends attack him, which makes Peter confined to a wheelchair and causes him to realize that handicapped people aren't really any different or less cool than the non handicapped.
In "German Guy", Peter and Chris are locked up in the basement of an old Nazi and there is a small window where they can call for help. They see Meg walking down the street. You'd expect: Peter and Chris to call for Meg and ask her to get them rescue. Instead: They make fun of her weight and ruin any chance of having her help them out. They end up getting Herbert to help them.
In the episode "Blind Ambition", Quagmire spies on Lois going to the bathroom and is clearly getting aroused from it. Lois spots Quagmire and freaks out, getting him arrested. Peter and the others meet up with Quagmire the next day to address what happened. You'd expect: Peter to punch Quagmire in the face ... or at least scream at him for watching his wife go to the bathroom and tell him to stay away from her forever or else. Given how jealous Peter gets whenever any man tries to talk to Lois (to the point that he ripped a movie screen while a Hugh Grant movie was playing and punched his own reflection), the writers could have used this bit of characterization to its fullest advantage here. Instead: Peter defends Quagmire and claims he is a good guy that is just screwed up in the head every now and then, ignoring the fact that A) Quagmire practically sleeps with every woman he sees and possibly rapes some of them and B) made Lois feel unsafe in the public bathroom.
In "Brian And Stewie", the duo are locked in a bank vault door with no way out. Stewie has his cellphone will him, but unfortunately, the battery is about to run out and he has to make one call for help. You'd expect: Stewie to call the police or firemen to get them out of there. Instead: Stewie wastes the one call to a department store to return a sweater.
In "Amish Guy", Meg falls in love with an Amish boy, but his father tells them not to see each other. When Peter confronts the father, he manages to get on his good side and is about to lift the ban. You'd expect: Peter to leave now that everything had been sorted out. Instead: Peter decides to "teach them about rock and roll" by taking out a boom box and playing the music at full blast. This causes the Griffins to get banned from the Amish village. Oh and the song that was playing? Highway To Hell.
"Movin' Out (Brian's Song)": Brian is convinced to move into an apartment with Jillian, despite his initial resistance to the idea. He comes to enjoy it, but cannot afford his half of the rent and has to have Stewie pay it for him. Eventually, Stewie, while being a Jerk Ass just because he has the option, reveals this to Jillian. You'd expect: Brian to just admit "yes, I can't afford the rent" and then maybe work on fixing that the next day. Instead: He acts as though he still does not like living with Jillian, since apparently Character Development means "character acts as he always has until the last five minutes". She then leaves him for Adam West. On a funnier note: The very next Cutaway Gag in the episode involves a baseball team that loses constantly because they insist on hiring a second baseman who has no arms. This is actually pointed out by the announcers in said cutaway.
"Family Gay": Peter gets injected with the "gay gene" and becomes a homosexual. Lois hears about it and is naturally shocked. She wants the procedure to be reversed but she quickly changes her tune when Peter starts to bake food and help her choose what clothes to buy. You'd expect: Lois to immediately realize that Peter being gay means he wants to have sex with men instead of women. Instead: Lois is shocked that Peter does not want to have sex with her and then realizes that Peter is actually gay and not being just an effeminate guy.
When Connie starts to date Chris just to make him popular, Chris falls in love with her and says that she is a really sweet girl. This makes Connie feel good about herself hearing that someone likes her for who she is and two of them start to date as an actual couple. You'd expect: Chris would stay with Connie and make the relationship work. Instead: Chris dumps Connie for two other girls because he thinks he can have any girl he wants.
In the episode "Internal Affairs," Peter gives Joe advice to cheat on Bonnie. You'd Expect: Joe would reject the idea for being bad and not do it because two wrongs don't make a right. Instead: He goes along with the idea and he gets caught cheating.
In the episode, "Friends Without Benefits," Meg is devastated when she finds out that her crush, Kent, is gay, and she still decides to win his affections. You'd Expect: Meg to realize that Kent is into other men and to find someone else. Instead: She plans to get Kent and Chris to have sex with each other. She has a Heel Realization, calls out the plan, and then Kent and Chris find out about her plan, and then Kent ends up hating Meg.
A basic staple in Family Guy's later years. Meg tries to make friends with the popular kids. You'd Expect: Meg to realize that the popular kids will never accept her and to find friends that actually like her for who she is. Instead: She keeps trying to make friends with them, and they end up insulting her and/or humiliating her in the most crushing ways possible. It's gotten to the point where Meg is cutting herself because of the psychological trauma over being rejected by the popular kids (though most of it can also be attributed to how her family treats her, which isn't much better).
In "Be Careful What You Fish For", Brian discovers that Stewie's kindergarten teacher is horribly neglective. You'd Expect: Brian to call the police and get her arrested. Instead: He falls in love with her and repeatedly refuses to do so. Stewie then gets a dislocated arm. Thankfully: The teacher turned out to have a boyfriend already, Brian gets her arrested for it and child neglectance.
Brian himself is partly to blame for his death in "Life of Brian". You'd Expect: While fixing the hockey net, Brian would have done it on the yard or sidewalk, where it is safe. Instead: He does it in the middle of the road, where that infamous car runs him over.