I don’t have to give you any examples of stupid things that Sarah Palin says. All I have to do is refer you to Saturday Night Live.
/s
SNL and Tina fey did a good job on their impersonation of Palin. So much so that the goofs that watch that show assumed that it really was Palin and the media did the same. They put Palin in a position of defending the idiocy of someone who was impersonating her.