Crisis on Earth-X, Part 3 - S4-E8
Stupidity: After the power cuts out, Thawne realises an obvious hiding spot and races to the secret room. He sees it's empty and just...stops looking? We literally just saw The Flash take a fraction of a second to scout out an entire enemy base we're told was 22km away! While he's dawdling in the secret room, Iris and Felicity get to Kara, knock out the guards, and get her down the corridor to the lift. He could have checked the entirety of Star Labs 10 times over in that time.
The Prison Prep School Murder Case File 2 - S1-E11
Stupidity: Akechi finds the pieces of chalk but does not investigate the open locker, where the victim left what turns out to be literally the name of the murderer. The plan of the all-knowing Puppeteer works only because the smart investigator does not perform even the most basic crime scene.
Stupidity: During a raid of a Latin stash house, Hailey and Kim find two girls with a pistol. In Spanish, they say no bullets. Kim interprets what the girls say and Hailey replies, l didn't know you spoke Spanish. Makes no sense that a partner on an elite police unit in Chicago would not know a member of the team speaks Spanish. (00:14:58)