
Stupidity: The fact that the young mother in the hospital would give Janet (a total stranger to her) her baby to watch while visiting her husband in a different area is completely unreal. Nobody would really ever just give their baby to a stranger like that and leave. In addition, Janet took the baby into Jack's room for quite awhile.

Stupidity: When they are conferring before surgery everyone is keeping scrub except for Avery who has his arms crossed. Shortly afterwards you can see him look around at all his co-stars, realise he screwed up and try to casually raise his arms. (00:15:00)

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.

Stupidity: The villain should've removed the tape hidden in the mask once he had it as it was incriminating evidence.

Stupidity: The whole episode revolves around Adam bringing his girlfriend Emma to his parents' house to meet the family, but problems start to arise when Emma's sister begins texting Adam pictures of her in her underwear. Adam is extremely bothered by this and attempts to make sure Emma doesn't find out. When everyone is at the dinner table, Adam decides to leave his phone out on the table even whilst he continues to receive texts from Emma's sister and the family begin to comment on it. If Adam was so concerned about Emma finding out about the texts, he could have easily turned off his phone and put it back in his pocket, but instead decides to leave it out on the table and switched on, only drawing more suspicion from Emma. Even when the little girl arrives later and asks to play with his phone, Jonny reaches out to grab it, but all Adam does is take the phone off the table so Jonny can't reach it, and then immediately puts it back on the table again.
Suggested correction: Adam knows Jonny is joking with him, as he usually does. As for Katie taking his phone he didn't expect her to. They have all seen Adam's reaction when getting the messages and he is trying to cover something up. Doing anything to prevent anyone seeing his phone more would arouse suspicion. Personally I don't understand why he didn't just explain that Emma's sister has been sending him pictures and ask Emma to talk to his sister. He didn't do anything and loses someone he liked for no reason.
I was mostly referring to the scene where they are sitting at the dinner table BEFORE Katie arrives. Despite the fact that he kept receiving texts from Emma's sister and was growing more concerned and everyone begins to comment on it, all he does is put it back on the table, switched on, ready for another text to come through, which makes everyone further suspicious. There is no reason at all why he couldn't just turn off the phone, put it back in his pocket, and lowered suspicion.
A better idea would be for him to have told Emma after it happened the first time. I'm sure that saying "your sister just sent this to me for some reason. I'm quite uncomfortable. Could you please ask her why she's sent me this?" would have sufficed. He creates bigger issues by denying anything is happening.

First Kiss - S1-E2
Stupidity: When Jeff Malone leaves the sandwich shop, he leaves the sandwich on the table. It would have been very easy for them to tell what was on the sandwich without needing to wait for Max to get home to recreate it. (00:02:41)

Stupidity: When Eddie finally finishes installing the VCR and it explodes, they get a man out to repair it. However, Eddie had previously told Richie that he'd stolen 60 VCRs; 17 in the living room and another 43 in the attic, so they could have used one of the other 59 and saved themselves a crate of Malibu.

Always a Godmother, Never a God - S6-E4
Stupidity: Rory arrives in Star's Hollow for the baptism. She parks presumably near the church. When she gets out of the car, she does not have a purse or car keys in hand. She apparently left the car unlocked and left the keys in it. It's just plain dumb.

When in Rome - S1-E3
Stupidity: A supposedly covert camera is placed in plain sight on a wall in a crowded room, with a prominent antenna showing, and a blinking blue light. (00:16:55)

Stupidity: In the flashback, Emily's sister takes ill while playing her flute. In the next scene, the sister is sick in bed and Emily now has the morpher around her neck, but she is in the exact same outfit. If the sister was forced to pass the legacy on due to disease, it should have taken more than just a few minutes or even hours to learn that.

Is Lupin Burning... ?! - S1-E1
Stupidity: Despite the fact that there are 100 (literally) cameras around the racing circuit and (again literally) everyone from the staff to the fellow racers works for the Scorpion gang, Jigen and Lupin's switch can happen without anyone noticing, even if it involved racing side by side for a lengthy period of time.