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 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.