THE LENGTHENING delays and hesitations by the White House, on the dozens of top appointments still to be made, are beginning to interfere with orderly government. President Carter wants to be careful about these appointments - very, very careful. It's a process that demands care. But there is such a thing as being careful a fault.

A new administration is entitled to a bit of time to get itself together. But Mr. Carter has now been in office six weeks, and there are confirmed by the Senate but the Secretary. Dozens of people have been called to Washington by the Carter administration for jobs to which the White House has yet formally to name them. Many of these people are at work behind desks to which they are not legally entitled, under titles that they have to deny. As an expedient for the very short term it is permissible, but it's gone on long enough now to get in the way of the business of government.

The trouble does not lie in Congress. On the contrary, some of the congressional committees have tried to force the pace a bit by holding hearings on people whose nominations the President has not yet formally submitted. One or two committes have even begun inviting testimony on plans and programs from officials who have not yet been confirmed. Neither does the trouble lie in the department, where in neary every case the names and faces of prospective nominees are already familiar.

The trouble is at the White House. In case after case, if seems that the papers are on someone's desk - waiting. For what? Further clearances, further inquiries, further consideration. Mr. Carter has evidently given so great an emphasis to the need for 100 per cent assurance of clean records that his staff is moving through the approvals with a degree of extreme caution that keeps bringing the process to a standstill. Whatever the full explanation, the result is an enormous back-up of pending nomination at the White House. A few examples:

At the State Department, only two officials - Secretary Cyrus Vance and his deputy - have been confirmed. Since the deputy is currently out of the country, Mr. Vance is required to waste a good deal of his time on routine chores - like signing his name, over and over, to routine documents - that no one else in the department is yet legally capable of doing. T hese personnel delays are particularly unfortunate in diplomacy because the under secretaries and assistant secretaries deal constantly with foreign governments that neither like nor understand the ambiguous status of people who have been named within the department but not yet nominated and installed by their government. There are some 16 names of State Department designees now waiting clearance at the White House before going to the Senate for confirmation.

At the Defense Department, only four officials have been confirmed: the Secretary of defense, his deputy, and the Secretaries of the Army and the Navy. No one else. Several others have been nominated. But around a dozen are awaiting White House clearance to be named.

The Department of Health, Education and Welfare is under a presidential deadline to produce a welfare reform program. But there too only the Secretary has been confirmed. The confusion over appointments compounds the intrinsic difficulty of management.

At the Treasury Department, two have been confirmed: the Secretary and the assistant secretary for tax policy. It is particularly hazardous to leave open the office of the Under Secretary for Monetary Affairs. It is a negotiating job, in a specially that requires very fast responses. The international monetary system is going through a perilous passage. The President announced before the Inauguration that he would nominate Anthony Solomon for the job. But he has yet to send the nomination to the Senate. That leaves Mr. Solomon - and the office, and its responsibilities - in limbo.

At the Department of Housing and Urban Development, the only official confirmed so far is the Secretary, Particia Harris. She's had to do all the congressional testimony for the department over the past month. The under secretary, seven assistant secretaries and general counsel are all in various stages of twilight. Their deputies, Ford administration holdovers or career civil servants, are all "acting." They have their counterparts all over Washington - some of them being paid as consultants by the day, some of them still paid through previous government jobs.

Commerce and Interior are other departments where no one has been confirmed but the Secretaries.

At six weeks, it begins to be a bit late for this kind of thing still to be going on. For a President who gave great emphasis to brisk and orderly management, it is decidedly late.