No, Google should not delete the image, but they probably should allow users to 'vote up' or 'vote down' images, like they do with websearches. This way, the image would normally disappear quickly, unless of course many find the image very funny (which I don't) or vote it up in a joint effort to damage her.

Google hardly filter pictures at all, unless they are obviously unlawful.
They show swastikas, as those are not illegal, not even the ones used in Nazi German flags. However, they do filter out child porn (I haven't tried that one though, I really HOPE they filter that out).

That aside, this DOES show that even Google can be manipulated to become a political tool, if a large and determined enough group puts in a large enough effort. The 2008 presidential elections have shown that this is clearly the case ('Obama is a communist', 'Obama isn't born in the US', and many others), and this clearly shows that even Google results should not always be taken for granted.

Google is a search engine, and as such, it is an information/research tool. It is NOT their job to police content for me. If enough viewers deem the "monkey" image irrelevant and inappropriate (as I do), then Google's algorithm should cause it to disappear from the search result. If this doesn't happen, then it is a fault of Google's algorithm and technology, not their standards or corporate ethics. The only material I would think Google should outright remove from their results would be material that is illegal, such as instructions for building a nuclear device or a direct incitement to violence against an individual or group.

NO. I think it is not google's problem, google for most of the users is just a tool gathering info, doing analysis and displaying result. Only if Frist Lady asked google to do so or googlel should keep it there.

Things is, google is not a free tool only, goolge is a corp, making money is main purpose. It has to following different regulations to win more customers and money.

They shouldn't but it looks like something happened because I cannot even find that image anymore in Google Image Search

No! Censorship is always bad in every case. I don't believe google should even operate in china where things like this are regulated. It would be impossible for any search engine to regulate every offensive image. And the definition of offensive isn't an objective thing. They can however filter illegal content, that is a different thing than distasteful. The only thing that I know of that is illegal on the internet is child pornography. Even child pornography is not that simple to regulate when dealing with international content. The rules for that are different in every country. Under 18 is illegal in some countries while 16 is the law in some countries. This was recently a big problem in the US when nude images of Daniel Radcliffe (harry potter) started showing up online in England where it was illegal (he was 17 years old) but the same images were illegal in the US (18 is the age there). The internet is still the wild west! There will need to eventually be some consensus, perhaps an international organization who looks at legal issues, bu tas far as content that is offensive goes no that should not be regulated, I would hate to live in a world that was so sterilized that everything was so politically correct.