The only real stupid decision is to publicly threaten the Mandarin. Pretty sure up to that point the tabloid press and every other major media outlet knew where he lived but once it declared it on live TV it was okay to invade the privacy they once voluntarily gave the heavily armed flying man with impulse control issues.
Threatening the Mandarin wasn't in and of itself a stupid decision. The stupid decision was to not immediately get in one of his suits, and to have a buggy prototype on standby instead of a fully functioning one.
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Yes he ended up putting Pepper in harms way. Yes, he put the kid in harms way. Yes, maybe he should have called SHIELD once he met the Extremis soldiers (you can't tell me that power wouldn't constitute an international threat). And speaking of SHIELD why wouldn't Capt. America be all over this Mandarin problem. Isn't tracking down and punching guys like this repeatedly in the face his bailiwick? I digress.
The existence of S.H.I.E.L.D. is why the this movie's premise falls down immediately. What happened to Nick Fury? Was he golfing?
I can't think of any other "stupid" decisions he made other than the two I outlined.
Okay, here's one: destroying all his suits at the end of the movie. What's he going to do in the next Avengers movie? Consult?
Here's another: his combat tactics were just plain baffling. The first time somebody melted off a piece of his armor, he should have never gone toe-to-toe with them ever again. He was in a flying suit with ranged weapons, and yet he chose "punching" as his main combat offensive. And then when he remembered he had ranged weapons, he decided to use them up close (ahh, memories. "Does anyone have an Awaken they can spare?"). The delay it took for a repulsor to charge up, announced by an escalating whine, meant the folks with the superhuman reflexes could see this telegram coming, read it, ball it up, and attack first.
Then there was the whole "not seeing a therapist for my anxiety attacks, even though I could pay one for a year with the interest I earn in a minute." Yeah, I get that he likes to shoulder burdens on his own. That strategy nearly killed him in IM2. He's supposed to be an off-the-charts-level genius, so making the same kind of potentially fatal mistake twice shouldn't be something he does for that reason alone, let alone this thing called "character development" that the scriptwriter apparently never heard of.
The plot holes were even worse, but that's another post.