The Succubus (a.k.a. Chef's Mama) - S3-E3
Stupidity: When Kenny and Cartman are sitting on the bench, Cartman can't start the tape as he has fallen asleep. Kenny then tries to wake him up, but wouldn't it have made far more sense for him to just start it himself, as he is sitting right next to it? Cartman's job was to push the play button. It was not like he had to rewind, fast forward or even eject the tape, so all Kenny had to do was just simply push the play button and tape would have started to play.
It's Not Easy Being Green - S5-E16
Stupidity: Unless the tow truck was someone else's or Hank had the keys surely Dale and Bill could've used it to drive Boomhauer's car back.
Stupidity: At the start of the episode, the Brunnen-G planet is about to be under attack by His Shadow in a big ship that is capable of destroying the surface of the planet and everybody on it in under a minute with its fire power. It seems the Brunnen-G had time to respond, seeing as they send a counter measure against His Shadow... Except that they only send a single squadron of 6 fighters. Their planet is about to be obliterated by His Shadow's killer ship, and they only send up 6 fighters. And of course, they fail and all die except for Kai. (00:01:45)