It's practically a given for many farces and comedies of manners that "Everyone must, at all times, be shackled to an idiot ball until the last few minutes of the final act." Occasionally varied by inserting an Only Sane Man character whom no one will listen to.
All of the tragedy is a result of Antigone deciding that burying Polynices is more important than her own life.
Though this is less about her being an idiot and more about period-specific values. At the time, it would have been seen as completely logical to risk execution in service of the gods.
Creon for not knowing that, generally, flipping off the gods by not burying the dead is a bad idea.
Ismene gets it a bit when she decides to take joint responsibility, despite the fact that she did not take part in the crime. Although she makes it pretty clear she knows the likely outcome.
Arsenic and Old Lace: Officer O'Hara gets to hold it, especially after seeing Mortimer tied up upon his return to the Brewster house. Dr. Einstein tries to pass it off as something Mortimer was demonstrating as happening in a play (which is actually somewhat accurate), O'Hara refuses to untie Mortimer until he's had a chance to explain his play!
Doctor Faustus: After being humiliated by Faustus, the knight Benvolio gets a group of knights together to get revenge. Against the scholar with a demon slave and all the powers of Hell. It goes about as well as you'd expect. Faustus more than qualifies as well (see Badass Normal, Informed Ability, and Misapplied Phlebotinum).
Il Trovatore: The main characters play hot potato with it all over the place, but Leonora is the biggest offender. She agrees to marry Luna to save Manrico, but takes the poison before securing his release and, naturally, dies before getting him free. Genius, right there.
La Cenerentola: Prince Ramiro. In Act I, Cenerentola tries to explain her difficult family situation, with "a father who isn't a father" and her two half-sisters. Alidoro later appears and asks about Don Magnifico's third daughter. In Act II, Ramiro is surprised by Tisbe and Clorinda's terrible attitudes because Alidoro told him to look for his bride in Don Magnifico's house. He witnessed all that and still utterly fails to put two and two together.
Little Shop of Horrors: After killing Orin, Seymour indulges in what has to rank among the worst murder coverups in the history of fiction. He leaves his baseball cap and his bag at the scene of the crime (the bag, by the way, has the name of the shop on it), stuffs Orin's uniform in the trash can outside the shop, and doesn't even bother to clean up the blood he spilled on the shop floor. When questioned about it, he says, "I spilled some Hawaiian Punch and it stained."
Othello: Partially, anyway. Though the plot isn't completely driven by certain characters' stupidities, most non-Iago characters are completely and conveniently stupid whenever it supports the short-term plot.
Othello, suspecting Desdemona, questions Emilia, who has been with Desdemona basically from Act 1 onwards, whether his wife had cheated on him with Cassio. She says no. He then asks Desdemona to promise him that she hasn't cheated. She does. He decides not to believe either of them, which, one could argue, is proof of Iago's amazing skills of manipulation, but considering that the bulk of the play takes place over three days in Cyprus and Cassio and Desdemona haven't even had a chance, it kind of suggests Othello's being a little bit silly.
Desdemona has promised Cassio that she'll plead his case to Othello to try and get him re-instated. Perfectly fine. Desdemona proceeds to do so, insistently and constantly, ignoring things such as timing, tact, and Othello's mood at any given moment. She is also vague about the fate of the handkerchief when being direct probably would have served her better.
One of the most important motifs in the play is the Handkerchief, Othello's family heirloom that he gives to Desdemona, and which becomes a symbol of all sorts of things, but particularly her innocence and faithfulness. Desdemona drops this on the floor directly in front of Othello. Nobody notices.
Roderigo is possibly the most stupid character in anything ever, and his stupidity directly facilitates Iago's plotting. He goes and gets smitten with Desdemona (who, given the era, is probably between twelve and sixteen years of age), and so follows her and her newly-wed husband (a big scary general) to a war-torn country in an attempt to win her back. In the meantime, he is played as a complete pawn, not only personally funding Iago's schemes, but also getting stabbed as a fundamental aspect thereof.
Cassio has a genius idea; flirting with his boss's wife, continuously.
Rigoletto: The latter two-thirds of the opera, along with all the tragedy, hinge on Rigoletto grasping the idiot ball firmly with both hands and dashing for the end zone, and spontaneously forgetting what his own house looks like. Rigoletto is dragooned by the Duke's men into helping abduct a woman who has caught the Duke's eye (who is also, unbeknownst to everyone, Rigoletto's daughter), and goes along with it, at no point reflecting over how similar the place they're raiding is to his house.