From my perspective, the big problem with Christine Lagarde as head of the IMF is that she is very likely to step the IMF away from its current--correct--technocratic position that the global economy needs easier money and more government spending in the core and replace it with Euro-austeric policy nostrum snake oil, to the world's impoverishment. I think that this is behind Martin Wolf's worries too, but he focuses more on procedure:
Europe should not control the IMF: Gone are past promises of an open selection [for IMF Managing Director]. The Europeans insist on the principle that what we have we hold. The ancien régime survives. Mme. Lagarde is a perfectly respectable candidate. She is French, almost a requirement, it often seems, for the European head of an international institution.... [S]he is not a perfect candidate: her economics are limited. If she were to become head of the organisation she would have to rely on the advice of those around her. If she were to get the job, it would be essential for whoever replaces John Lipsky, the American first deputy managing director, who is due to depart in August, to be a first-rate economist.
I write as if she is going to get the job. I am quite sure she is. As of today, the European Union still has 32 per cent of the votes (see chart) and the US another 16.7 per cent. If the latter supports them, as I suspect it will, the Europeans will have no difficulty in obtaining additional votes.... Why might the US support the Europeans once again? One reason is that the US has not yet given up on the old bargain, which gives it a permanent lock on the presidency of the World Bank. Indeed, the Americans will probably tell themselves that the chances of getting any money from Congress for World Bank programmes (above all, its concessional lending arm, the International Development Association) if the Bank’s head is not an American is close to zero. To be fair to the Europeans, the emergence of the IMF during the course of the current crisis as... a European monetary fund gives an understandable urgency to their desire for control.... The Europeans’ argument is, in my view, stronger than these critics will admit. The eurozone is a very special (and, in my view, quite dangerous) construction. When the IMF lends to Greece, Ireland or Portugal, it is directly affecting the monetary and financial stability of all other members of the eurozone. It is almost as if it were rescuing, say, California from a looming default. It is, I think, understandable that leaders of powerful countries, such as Germany or France, want to feel complete trust in the management of an institution that is performing such a vital function for themselves.... While I find this European argument has some force, it does not have enough force. The counter-argument is that it is in the Europeans’ interest to receive unbiased and independent advice from the IMF....
On balance... one has to recognise the enormous advantages in terms of the global legitimacy and effectiveness, not just of the IMF, but of the multilateral institutional order, of making a transition to open global selection of the IMF’s new head.... The best course, I believe, would be to commission a high-level search committee. Candidates should also set out their prospectus for the future of the IMF: there are many big issues ahead, including global monetary reform. They should then be chosen by the members on merit. The criteria used should, however, be far more than technocratic. An understanding of economics is indeed important. So, too, is proven political ability, toughness and experience as a successful high-level policymaker. The person chosen should be willing to take the risks of leading.... Regimes that do not bow to the winds of change get blown away. The Europeans need to recognise that truth in time. They will not do so. But it will prove a big mistake.