How can the blockchain help?

I think it would be very good if all government income and expenditures were done on an open blockchain, and with the accounting openly available so everyone could see how the money is spent. Receipts and contracts should also be openly available (generally - exceptions do apply - but far too often secrecy is the norm and openness the exception).

This would help quite much against embezzlement, and it would help bring light to dodgy tenders, but it would be no silver bullet neither against the more advanced forms of corruption nor against the very low-level form of corruption; a monetary reward directly from person A to person B, and person B doing something favorable for A in return (i.e. traffic cop B stopping car A for some traffic offence and then just waving the car further).

Of course, unless you want all transactions attributed directly to identified people and openly visible. For privacy reasons that's probably not wanted. (but it's still probably a lot better than transactions that are hidden for most folks, but plainly visible for banking employees, government officials, computer security crackers, etc