The Federal Home Loan Bank Board, which oversees the vast, $400-billion savings and loan industry, nearly went out of business last week for lack of quorum on its three-member board.

Only a last-minute, 31-day extension of the expiring term of member Grady Perry, and Democrat Perry's willingness to stay around an extra month, will keep the bank board functioning in July.

But if Carter's nominee - Naval Academy classmate and political ally Robert H. McKinney - faces any problems in the Senate, the administration may again find itself threatened by a temporary shutdown of the board.

McKinney is opposed by many civil rights and activist groups who contend that he is insensitive to the mortgage needs of the inner city as well as to conflicts of interest. McKinney is chairman of First Federal Savings and Loan of Indianapolis.

Senate observers, however, think that McKinney will approved after tough confirmation hearings later this month.

The near-breakdown of the bank board is only the latest of several instances where the new administration seems to have paid little attention to appointments to the little-known, but powerful agencies which oversee the giant U.S. financial industry - from the mortgage-oriented savings and loan associations to the commercial banks.

Only a month ago, after more than four months of inaction on the part of the administration, Robert A. Barnett, the outgoing chairman of the Federal Deposit Insurance Corp., took the matter of his successor in his own hands.

At the Federal Home Loan Bank Board, the President names the chairman from among the three board members - who are all presidential appointes confirmed by the Senate.

At the FDIC the chairman is elected by the board itself.The FDIC board is composed of two presidential appointees and the Comptroller of the Currency, in an ex officio capacity.

Normally, when an FDIC chairman resigns the comptroller becomes acting chairman until the new member comes on board. The FDIC regulates thousands of state-chartered banks and insures deposits up to $40,000 in nearly all banks. The FDIC usually acts as receiver when insured bank fails.

Because the Comptroller of the Currency, Robert Bloom, has been in an acting capacity since last summer, Barnett was unwilling to have him become acting chairman of the FDIC as well. Among other things, it might make the agency vulnerable to shareholder suits during failures.

Ironically, the man Barnett nominated and then voted for as his successor, fellow board member George A. LeMaistre, is a Southern Democrat with impeccable credentials who has been the administration's choice to head the agency all along, although officials had never done anything about it.

Carter has not yet nominated anyone to fill Barnett's job. But in late May, he nominated former New York bank superintendent John G. Heimann to become comptroller of the Currency.

The comptroller regulates the nation's 5,000 nationally chartered banks.

The close-call at the bank board was disconcerting to many because McKinney apparently has been Carter's choice to head the agency for some time. The administration was aware that Perry's term would expire June 30, leaving the board with only one member, Republican chairman Garth Marston.

Last winter, some observers thought Carter would nominate Perry for another term to serve as chairman. Rep. Ferdinand St. Germain (D-R.I.) also was mentioned then.

McKinney was reluctant to take the job at first, sources said, but when consumer and civil rights groups protested the potential appointment, he decided to accept the President's nomination.

One other important and lucrative job remains open: that of president of the Federal Home Loan Mortgage Corp., which buys and sells home mortgages to keep financing available. The $60,000-a-year job needs no Senate approval only that of the chairman of the Federal Home Loan Bank Board.