The first thing politicians do when other politicians publish memoirs is look themselves up in the index, but here's a piece of advice for David Cameron:

do not read what Hillary Clinton has written about you in her memoir. Gordon Brown should probably avoid the book too. And the former Labour minister David Miliband. In fact, anyone with a low embarrassment threshold should avoid the section on David Miliband.

The reference to Cameron comes late in the book, which covers Clinton's four years as US Secretary of State during Obama's first term as president. "President Obama and Cameron took to each other right off," writes Clinton, "They had an easy rapport and enjoyed each other's company." And what of her own views of the PM? "Cameron and I met together a number of times over the years" - a sentence that presumably follows the traditional advice of grannies and diplomats that if you can't say anything nice, say nothing at all. Unless it doesn't mean anything of the sort. That's the point of diplomatic language: you can deny that it means what everyone thinks it means.

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The references to Brown and Miliband are more explicit, in the case of Miliband a little too explicit. Brown gets Clinton's pity ("I could see the strain he was under") while Miliband gets her praise. In fact, she lists his qualities as if quoting from his profile on a political version of he is young, energetic, creative and attractive, she says. It's embarrassing, but not as embarrassing as Miliband's fawning comments to Clinton when she became Secretary of State. "It's a Herculean job," he told her, "but I think you're the right Hercules for the task."

Strangely, that reference to Miliband is one of the few emotional sections in a book that is otherwise far too cool and careful for its own good. Clinton's aim is to cover most of the major decisions she took as Secretary of State - the Hard Choices of the title - but she does so far too diplomatically and cautiously. This is probably because Hard Choices is not a typical political memoir written by someone who has left office for good; it is a memoir written with one eye on office in the future, which means the language is careful. Whether being careful is what will win her the White House is another matter.

She does address the issue of her potential candidacy directly but not until page 595 and even then it's not really an answer to the question "Will she run?". She tells us that she hasn't decided yet, although one of the probable reasons for writing this book is to clear out the cupboards before a possible attempt at the White House. Better to deal with some of the lingering issues from her time as Secretary of State now than have them surface during a presidential campaign.

The most obvious issue that needs dealt with is Iraq, and Clinton says she regrets supporting the decision to invade. "As the war dragged on, with every letter I sent to a family … who had lost a son or daughter, a father or mother, my mistake became more painful," she says. Who knows if this regret is genuine or not, but with insurgents seizing the Iraqi city of Mosul in the last few days and pushing to seize more of the country, it feels like one of the most open and relevant sections of the book.

The section on Syria is more troubling, possibly because it hints at what kind of president Clinton might be. If we are to prevent the danger of terrorist attacks launched from Syria, she writes, we must arm the rebels. This was the case she put during her time in government but she was overruled by Obama. Perhaps he will be proved right in the long run, or perhaps the longer the crisis is unresolved the more Clinton's case will seem convincing.

This tough approach from Clinton does not necessarily mean she would be a hawkish neocon as president - indeed, the domestic Clintonian philosophy that emerges in the book is liberal and inclusive, although she is keen on the essentially right-wing idea that civil society should do as much as government (Cameron called it the big society). A healthy society, says Clinton in one of her occasionally folksy moments, is a three-legged stool, supported by responsible government, an open economy and a vibrant civil society.

She also makes it clear she believes in the idea beloved by Americans that more freedom brings greater prosperity. This would undoubtedly put her to the right in British politics, but there is a great deal of idealism in her too, particularly on women's rights and gay issues, and pragmatism ("work for the best outcome but plan for something less"). She describes her approach at one point as idealistic realism but the critical question is whether that's an exciting enough philosophy to win her the presidency.

The fact there is not more to get excited about in Hard Choices is not a good start. The best political memoirs are written by those with nothing to lose (like Tony Benn's) or those with a score to settle (like Margaret Thatcher's) or those who just don't care (like Alan Clark's). Hillary Clinton's is none of those, but she could at least have filled the void with a vision. There's still time.