Why was Alexei Kudrin nominated by Putin as the Chairman of Accounts Chamber?
Chairman of Accounts Chamber looks over goverment plans of spending budget for all sides of country's improvement and maintainance - industry and research supporting, military, farming and so on. It is an auditor in fact, which reports direct to president.
Alexei Kudrin don't have good relations with Medvedev's goverment, so, it is an ideal auditor for goverment's actions. With such auditor, Putin can be much more calm about goverment's spendings.
And it have already some results: on its last report in Duma(Russian pairlament) (http://www.interfax.ru/amp/617726), he claims about untargeted budget spendings in space program, so Investigation commitee already started deals over it.