The Return of Hydro-Man: Part 1 - S5-E7
Stupidity: When Spider-Man is working in the lab, he uses his webbing to barricade the door shut so no-one interrupts him. When Debra Whitman shows up and asks who is in there, he identifies himself as Peter Parker. When he is finished with his work, he leaves out of the window so that by the time the security guards break the door down, he has vanished. Since he used his webbing to keep the door closed, it would be pretty easy for Debra and the security guards to figure out that Peter is Spider-Man since Spider-Man's webbing is at the scene and Peter seemingly vanished into thin air.
Behold, a Distant Star - S2-E10
Stupidity: When Johnny finds out his father is alive and wanted for murder, he is livid with his sister for telling him neither fact. When Sue decides to tell him the whole story, she asks Reed to pull a photo album from the drawer next to him, which contains a newspaper clipping detailing that their father was wanted for murder. If Sue didn't want Johnny to know about that, she shouldn't have placed the clipping in a photo album, and then kept the photo album in a communal area where Johnny could have easily discovered it at any time. (00:06:19 - 00:07:34)
The One With All The Rugby - S4-E15
Stupidity: Emily tries to help Ross inflict pain on the other rugby players and tells him about one player who doesn't wear a cup. No one who knows rugby would ever wear a cup, it is more hazardous than helpful to wear a cup in rugby as it involves a lot a grinding, and a simple slip or movement could cause serious damages to the male genitals. Especially if these guys are British and well versed in rugby which they are.
Iron Man to the Second Power: Part 2 - S1-E10
Stupidity: When the other heroes are watching Iron Man battle his robot duplicate, Julia cheers him on and calls him Tony. This fight is taking place in full view of the public, and the public doesn't know that Tony Stark is Iron Man. They believe that Iron Man is Tony Stark's bodyguard. Julia could have easily revealed Iron Man's secret identity in this moment. (00:17:50)