Stupidity: When the bellhop is in the elevator and it looks like this is where he loses his arm, he spends a few minutes trying to stop the elevator. All he had to do was let go of the luggage and he would have been able to easily bring his arm in.
Stupidity: Cobb convinces Fischer to enter a dream saying it's Browning's dream. A couple of scenes later he says it's Eames' dream, in front of Fischer, who doesn't know Eames was impersonating Browning. (00:51:35)
Suggested correction: Firstly, the Browning that the team "catches" is not Eames, it is a projection of Fischer's subconscious. Eames was only impersonating Browning in the first level. Secondly, Cobb doesn't say they are going into Browning's dream, he says they should put him under and do to him what the kidnappers were planning to do to Fischer. That is, use Fischer as the subject of the next dream level. Fischer knows that Eames is the dreamer on the third level, he even jokingly asks why Eames couldn't dream of a beach. But he thinks that Eames is part of Mr. Charles' security team. He believes that Browning is to be the subject on the last level when in fact, Fischer is the subject on each level. Because of how effective the Mr. Charles gambit was, Fischer is unaware that the team has been fighting his subconscious all along.
Stupidity: Jake throws Derek overboard to distract the piranha, then swims under the boat and doesn't get attacked, so why couldn't he just go downstairs the normal way and have Kelly swim over to him? They could have escaped a lot more easily.
Stupidity: Why in the world would Tony of all people leave his old suits in storage WITH the miniature arc reactor still inside the suit? This would have served no purpose to Tony since he already has his own arc reactor in his body.
Suggested correction: This is a question which is easily answered; Tony had the idea of putting someone else in the suit (like Rhodey) himself. Plus, it's logical to think he has built multiple miniature arc reactors, after the events of the previous movie. Plus, he can probably just as easily switch from arc reactor to arc reactor in his chest when changing suits, so he has a fully powered arc reactor ready in each suit.