Stupidity: During one of the test drives, the hook that Hiccup uses to fasten himself to Toothless gets bent, so he takes Toothless to the blacksmith to cut the line. There are two ways he could have easily avoided this: He could just unhook the saddle, take that to the blacksmith and cut himself loose, or he could just untie the leather strap. What he does here is needlessly risky and just there for his awkward conversation with Astrid.
Stupidity: When Harry finds the Sword of Gryffindor at the bottom of the frozen pond, he breaks a man-sized hole in the ice, then strips down and jumps in. He could have broken a far larger hole in the ice, negating the risk of being unable to locate the hole upon coming back up. But because he doesn't, he nearly drowns when the locket resists and he can't surface (he couldn't have anticipated the locket's resistance, but that such a small hole would be hard to get out through was easily foreseeable.)