One is working out exactly what his boss - Tony Blair - really wants him to do with the formidable machine of which he is now titular head.
The other is personal. Will Wilson's legendary charm and good humour be enough to win over his fellow mandarins, particularly members of the "college", the secret committee of permanent secretaries who form the backbone of this and every government?
The college contains rivals and successors. At least two were candidates for his job - Sir Andrew Turnbull, John Prescott's permanent secretary at Environment, Transport and the Regions, and Sir Richard Mottram, permanent secretary at Defence, just knighted and still young enough to succeed.
One of the college's most senior members is now Sir Terry Burns of the Treasury, a man who knows both that he serves a political master on whose shoulders the success of the Blair administration rests and that his own fate depends on how well he advocates Gordon Brown's view of the world.
But Sir Richard brings some powerful weapons to bear, among them his own vast experience of the Treasury, the Cabinet Office and several mainstream departments, including Sir Andrew Turnbull's command at Environment. He knows, says a colleague, where the bodies are hidden. In addition, several members of the college are very new - the permanent secretaries at Health, the Home Office and Northern Ireland are only just in post.
He'll also be able to deploy the Cabinet Office's apparatus of patronage - including the power to appoint permanent secretaries and to decide who gets merit payments, bonuses, gongs and honorific appointments. Sir Richard's other problem is what to do with Whitehall. Tony Blair has said he wants "modernisation". Sir Richard will make noises about broadening civil service recruitment, especially of ethnic minorities (on which the Home Office, his own previous department, has recently been criticised). But his capacity to make structural changes, for example to secure better co-ordination between rival departments, is hampered by the power of his colleagues and increasingly fractious relations between the ministers they serve.
Privately senior civil servants say the paradox of Blair's Whitehall is that he may turn out to be weak, unable to impose his will and adjudicate the fierce territorial fights between Cabinet members. Just before Christmas a top man told me: "Sometimes I cannot make sense of the correspondence between Cabinet ministers, until I remember that most of them hate each other's guts with a passion."
Sir Richard has been compared to Orpheus, able to tame even such angry political beasts as former Tory home secretary Michael Howard. In the flesh he comes across as a genial, old time solicitor. He wins universal plaudits from his colleagues for his energy and manners. The press are going to find him uninteresting since his private life is spotless (he has just celebrated his silver wedding to his wife, Caroline), his hobbies include "country life and gardening" and he is unlikely to start investing his pounds 140,000-a-year salary in offshore trusts.
But however well qualified, Sir Richard may find his job may be impossible. He will have to act as a great-uncle to the young Blairites, offering advice and experience, while jumping to their every command. In the past eight weeks he has been canvassing his colleagues for reform thoughts. But the signs are that Tony Blair is a Whitehall conservative - the Prime Minister has hitherto been rather uninterested in administrative detail.
A colleague observed of Sir Richard that "he can shimmer without stain". But on welfare to work, social exclusion and other policies, lack of co- ordination between departments is the big Whitehall problem. The way forward is to create a powerful new machinery for co-ordinating policies, for example through a new powerhouse at the heart of Whitehall based on amalgamating the Prime Minister's staff with the Cabinet Office. To do that Wilson will have to prove that beneath the charm he is Whitehall's Mr Muscle.
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