Stupidity: After the accident, Dawn is in spirit form on the road trying to wave down an oncoming car (driven by Martha Kent). Dawn doesn't know she's a spirit that can pass through objects at that point. Since Martha can't see her, she keeps driving straight towards Dawn. Dawn sees the vehicle isn't slowing down and instead of simply stepping out of the way to avoid getting hit, she turns her back, revealing to the audience that objects can pass through her now.
Day 4: 11:00 P.M.-12:00 A.M. - S4-E17
Stupidity: When the couple is in the plant they call Jack on the cellphone, he instructs them to open the case and separate the book from the activation device. This was stupid, he should have told them to destroy it, since the codes had changed the moment Air Force One crashed, and it would take about 1 hour to make this work. This is explained later on in the show.
Stupidity: The last remaining Xindi, in desperation, attempts to release the virus over the fan, despite the virus not being fully ready. However, it seems the only reason he didn't release the virus at that time was he had to seek cover from Archer and T'Pol shooting at him and to start shooting back at them. However, he had plenty of cover from the rooftop stairwell, which was right next to the fan, and he had enough time to dump out the contents over the fan.