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Give people some kind of assurance that there isn't a way that the operator of the currency can just start minting bitcoins at will. It's probably irrelevant at the moment - but imagine if BC$ was as popular as e-gold in its heyday - the owner, if he were less than honest, could essentially be an Internet millionaire spending his own currency at will around the interwebs. In theory it's possible with any digital currency - but at least, the theory behind the digital gold currencies is that if all else fails, you can call them up and redeem physical gold (I'm referring to c-gold, e-gold, Pecunix, GoldMoney, and probably many others) so you have something 'tangible' as backup. What is BC backed by? Just saying, these might be things that a skeptic will ask himself before wanting to use this currency.
So the short answer is that BC is backed by mathematics/cryptography and the "wisdom of crowds"; assuming there's no flaw in the algorithms, and assuming that there is no grand conspiracy of more than half of the BC nodes, it is impossible to inflate the currency or make fraudulent payments.I don't believe in grand conspiracies, so that doesn't worry me. And I can't see any flaw in the algorithms... but that's where I'm skeptical (there might be bugs in the BC code, but those can and will be easily fixed).
Are there any professional cryptographers looking at Bitcoin?
Or will they only get interested if/when Bitcoin gets popular?