Hopes inside the Carter administration for better things next year have been boosted by this word coming out of the Oval Office: Jimmy Carter wants to rid himself of as much detail as possible in the second year of his presidency.

That is an unpublicized New Year's resolution both Carter cronies and key officials devoutly hope the President will not forget. The overflowing in-basket that has become the trademark of this presidency not only means Carter may be devoting too much time to the wrong activity; it is also viewed inside the administration and on Capitol Hill as a source of positive harm. Put bluntly, the President in solitary contemplation sometimes gets the wrong ideas about matters better left to the experts.

This remarkable fact tells much about bitter disappointments of the first Carter year felt by many of his supporters. Supremely confident of his own intellect, he had developed neither a top-notch White House staff nor a trusted kitchen cabinet of experienced counselors. This leaves no way to protect him from his own misinterpretation of the facts. Accordingly, his New Year's resolution to step back from the deluge of details is welcome news in the administration.

When Carter intimate Charles Kirbo visited here from Georgia recently saying how much older his friend looked, he echoed a prevailing theme of Washington. While the conventional holiday wisdom of 1974 and 1975 was that President Ford ought to cancel his annual skilling vacation and get down to work, the conventional wisdom today is that President Carter ought to let up on his work and get down to play.

Actually, there is divided opinion in his officially family about the seriousness of the President's workaholic affliction. Some officials point out he is seldom at his desk much after 5:30 p.m. and obviously enjoys weekends at Camp David. But others note that whenever and wherever Carter takes time off, he carries that ubiquitous file folder bulging with work - and actually plunges into it.

What worries everybody, in addition to whether the President is working too hard, is whether he is doing the wrong work. Beginning with the economic stimulation package nearly a year ago, Carter has probed and scrutinized every program with intensive, solitary study. The procedure reflects his abundant self-confidence and engineer's belief that he can master any situation by himself.

The danger of this is best shown by tax reform. Entering the presidency with his campaign litany that the tax system is "a disgrace to the human race" but with precious few details, he became immersed in a self-taught cram course on the Internal Revenue Code.

According to congressional tax experts, Carter got a few things wrong - dangerously wrong. The decision to set aside comprehensive tax reform because of the needed quick tax cut next year saves him from most such mistakes. But insiders report that as a self-educated tax expert, the President has checked the wrong box too many times on the option sheets.

There are hordes of tax experts at the Treasury and in Congress whose advice the President could tap. "But I ask you," one expert told us, "who is going to stand up to the President, look him in the eye and tell him, 'Mr. President, you've got this stuff you studied all wrong'?"

Herein is reflected a deeper problem of the Carter presidency. His White House staff is regarded as grossly deficient in organization and partially deficient in high-caliber talent. With Kirbo and Bert Lance both in Georgia, there is no peer who can look the President in the eye and tell him he is wrong. Carter is not happy over the way his time has been allocated this year. He has expressed dissatisfaction with the endless meetings selling the Panama Canal treaties and is now signaling that he really would like to delegate deskwork in a more traditional way.

He has asked Vice President Mondale to establish priorities for next year. This time he is devoting a mere fraction of the days spent on the previous year's economic review. Although he has studied the defense budget for unprecedented hours, this is supposed to be a one-time operation. Most important, the President has informed key officials he wants to see less paper in his in-basket.

The prospect of President Carter's spending less time in solitary contemplation cheers many officials. Looking further ahead, they would welcome more verbal give-and-take in the Oval Office and during increasingly antiseptic Cabinet meetings. But unfortunately that does not appear among his New Year's resolutions for 1978.