The Farting Sex Tourist - S1-E4
Stupidity: Joel finds prints in Serbian and is stressed because they'll never find someone to translate Serbian in Santa Clarita, goes to great lengths to interact with the principal's Serbian grandmother, etc. Google translate can understand Serbian just fine, but this doesn't even occur to him.
Suggested correction: Except the 16th century Serbian alphabet isn't available to most people to type into google translate. Plus the script used makes it difficult to distinguish which character is which sometimes even if you could find characters to cut and paste tediously into google translate.
Siege Protocol: Part 1 - S3-E11
Stupidity: The team is going on a CQB raid to free some hostages; so close quarters battle, room clearing, a very high chance of getting shot since the enemy can hide anywhere. They are not wearing plate carriers and their armor. This is the very mission that military doctrine emphasizes armor. It's not a long range patrol through mountains where weight matters. However on a previous mission to locate a downed pilot in open terrain they were wearing plate carriers. (00:27:12 - 00:28:00)
Through the Valley of Shadows - S2-E12
Stupidity: Burnham and Spock find one person alive from the otherwise-dead crew, miraculously. They know Control can infect humans, they know how advanced it is, the entire setup screams "trap", and yet they don't even question whether Gant even might be under Control's...well, control. A simple scan would have turned up anomalies and they could have avoided what followed.