Stupidity: An explanation is given for the reason why the bombs planted on the Gundam are not activated by remote control (they have plastic explosive in the regiment but not remote controls!), but no reason why they set the timer for the explosion to 30 minutes, way too much to be of any use in combat against the Gundam. Moreover, if the vulnerable spot of the Gundam shield were situated where it explodes at the beginning, it'd be completely useless.
Cucuruz Doan's Island - S1-E15
Stupidity: Amuro came to the island to respond to an SOS. He finds the pilots, tries to tend to their wounds, they die. He then meets a Zaku pilot that orders him to surrender. Amuro manages to jump on the Core Fighter, take off and then...tries a desperate and very hard maneuver to fight the Zaku, when at that point he simply needed to fly back to White Base; the Zaku could have never followed him. He has nothing at stake, no need at all to fight. And the Zaku pilot even told him that he did not want to fight to begin with. (00:08:00)
Stupidity: The Zeon commandos who plant the bombs on the Gundam correctly identify Amuro as the pilot. The Gundam is completely defenseless and pilotless during the whole bomb removal process - they could attack at any point and make the bombs explode shooting them like they did for the first one, but they just don't.
Coming Home - S1-E13
Stupidity: Amuro's mom is horrified by him shooting at the two Zeon patrolmen, and says it's "wrong to point guns at people", but was apparently completely oblivious of him being now a soldier and did not say a thing about it when he literally landed in the middle of the camp piloting a jet fighter, wearing his full uniform.