Sarah Palin dumber than a pillar box - the case for the prosecution
1) The question that floored her (about Kissinger and Iran) was an easy question. It was a closed question that could be answered with a variant on "Yes" or "No". It was also one of the most likely questions to come up - after Iraq, Iran is the foreign policy question that has been getting most traction in the American media, as well as an issue on which McCain has been attacking Obama. Palin has had a month to prepare for this interview, and this question would have been one of three of four key questions she had prepared answers to.
2) Palin is an experienced politician. She wasn't cracking up under the pressure of a (remarkably soft by British standards, although apparently normal for America) interview. She has been here before, lots of times. She was cracking up because she was being asked difficult questions she didn't know the answer to. Besides, if she cracks up like that under soft questioning then she isn't up to a job which involves a lot of negotiation.
3) There is nothing in Palin's background to suggest that she can think. Her degree is in journalism (she switched from business administration, another easy subject) from a not particularly good university. She dropped out repeatedly and took 9 semesters to complete a 4-year degree. The only real jobs she did before becoming a full-time politician were sports journalist and fisherman's assistant.
4) Palin does not come from a working class background. Her father was a schoolteacher, and could afford to send her to out-of-state private universities. She will have grown up perfectly aware that there were countries outside the United States, that books existed, etc. Teacher's children are massively over-representd among first-generation Oxbridge students because they grow up in a pro-intellectual environemnt. If a teacher's kid is a know-nothing, it is either by choice or becuase she is chronically dim. Neither is acceptable in a potential leader of the free world.
Femme-de-R also tries to claim that a man would have got away with being utterly clueless by "going on the attack". She assumes Couric is an incomptent interviewer, rather than a merely easy-going one. If Joe Biden in the same position had laid into Kissinger without answering the question, he would have looked like an arrogant moron. If he had laid into Couric, she would have coped (she is a professional) and he would have looked like a big meanie beating up the cute blond girl.
I agree with Femme-de-R that a significant number of dumb voters would have been fooled by the bluster. But they would probably have been fooled by the ditzy-chick act as well, as Femme-de-R was. George W Bush didn't get a free pass on being dumb, despite being a lot brighter than Palin. It was known at the time that he was too dumb to be President, which is part of the reason why he lost the election.
Both Bush and Palin get a lot of sympathy votes from dumb Americans who feel "represented". This is a bug in democracy, not a feature. If these people end up with President Palin (and McCain isn't getting any younger), they deserve it.