Lucifer, Stay. Good Devil. - S1-E2
Stupidity: It takes an awful lot of pointless visits and oblique thinking to simply investigate the known (and apparently only) collaborator and protege of the suspect, who also was on the crime scene. You'd think interrogating the business associate would be standard procedure.
Until Sunset, the Full Moon - S1-E7
Stupidity: This is not quite 'stupidity' but rather a "movie logic", supposedly sharp deduction that is really just a wild and nonsensical guess. Zenigata knows for a fact that Fujiko is impersonating Elena because she knew right away where to get the first aid kit, while Elena hasn't been in the mountain house since her husband's death. That makes no sense; Zenigata has to assume that Elena was completely straight about that fact (if it was the treasure's hiding place as he suspected, she easily could lie), and a person can easily remember where they store their security items even after years, for a variety of reasons.
Episode #1.2 - S1-E2
Stupidity: The part when the Colonel and the governess pose as journalists does not make sense. It's far-fetched enough that after a lengthy interview about the culprit's fortune the topic of his family never came up, considering it was one of the main goals and an ideal question to lead with, but considering that "mr. Todo" does not want a picture taken and has a tight security, there's no way that a photographer carrying a large 1930 camera would have been allowed into the interview room to begin with.
Stupidity: Despite being a high-profile fugitive who was a local celebrity in his previous life, Saul does very little to alter his physical appearance, settling on just a mustache and glasses. Growing a beard, wearing a hairpiece, and altering his speaking voice around others would have gone a long way in preventing him from being made.
405 Method Not Allowed - S4-E5
Stupidity: Elliot and his crew are trying to take down the Dark Army and Whiterose, they are being monitored by them via surveillance vans which Elliot just burned, etc. However, with Elliot and friends trying to be secretive he somehow manages to text Phillip Price on his cell phone about Tyrell. Phones are the easiest to intercept. Whiterose doesn't trust Phillip and plans on killing Elliot once their projects transferred to Africa. (00:07:20)