The third White House Conference on Aging, which has its first working session today, follows in a distinguished tradition.

The first aging conference, held 20 years ago, produced Medicare. The second, in 1971, resulted in added Social Security benefits for retired persons and extension of the mandatory retirement age to 70.

Given the jockeying and arguing that has preceded it, however, this conference's most signficant product may be a large political headache for the Reagan administration.

Before the conference opened, the administration found itself embroiled in disputes with organizations concerned with aging over procedural rules, delegate composition and allegations of general administration tampering designed to produce a result in harmony with the administration's goals.

Controversy and bitter political disputes are not new to White House conferences, but this aging conference is the first in which the administration in power has taken or is believed to be contemplating a broad range of actions that would be harmful to the people whose problems are to be under discussion.

Barring some last-minute agreement that will head off a confrontation, the more than 2,000 delegates to the conference may find themselves at the opening morning's program, intended to be largely ceremonial tone-setting speeches, dealing with an attempt by organizations on aging to stage a bruising fight to amend rules announced Friday by Health and Human Services Secretary Richard S. Schweiker.

The fight probaby will not result in the rules being changed, but the mere prospect that it may occur typifies the atmosphere of raw nerves and ill-feeling that has developed around this conference even before it began.

Rep. Claude Pepper (D-Fla.), chairman of the House Committee on Aging, already has accused the administration of trying to "pervert and prostitute" the conference in order to prevent it from taking positions against "the disastrous impact that President Reagan's Social Security and budget proposals would have on the elderly."

The Republican National Committee sponsored a poll of conference delegates, ostensibly to see if older Americans knew the president's positions. Officials of organizations on the aging, however, have charged that the poll was part of an administration effort to stage-manage the conference.

Last Wednesday, the leadership of the country's major organizations on aging called a press conference to warn that they might walk out of the gathering if Schweiker did not permit the delegates to vote separately on each of the 14 committee reports that will be made at the conference's last session Thursday.

Schweiker rejected the request Friday, but "has met us more than half way" on other points, according to Jack Ossofsky, executive director of the National Council on the Aging. Although Ossofsky said the single up-or-down vote on the committee reports still "is a matter of concern," a well-placed source said the prospect of a mass walkout was unlikely.

Ossofsky, who played a key role in the second White House Conference 10 years ago, spoke in glowing terms of the openness of the Nixon administration in its approach to the conference and the spirit of cooperation that existed between it and organizations on aging. "Now every recommendation is treated by the administration like an attack on the conference. It's a completely different atmosphere," Ossofsky said.

In addition to the different atmosphere, the political, demographic and fiscal realities are significantly changed from 10 years ago. The delegates are meeting in an age of fiscally diminishing expectations. In fiscal 1982, the combined cost for Medicare and the old-age portion of Social Security benefits will be between $190 billion and $200 billion.

Older Americans now are a significant, organized political force. The National Retired Teachers Association and the American Association of Retired Persons claim a combined membership of 13 million. The Reagan administration already has discovered how stiff and fierce opposition can be to tampering with Social Security benefits for the elderly.

Perhaps because of this potentially hostile atmosphere, the administration has been wary about preparations for the conference. Several former members of the conference's staff, all of whom have asked not to be identified, have spoken about an atmosphere of distrust and suspicion that grew after the Reagan administration took over the planning of the conference from the Carter administration.

Other signs indicate either bad planning or deliberate stalling by the conference's directorship. Selection of committee chairmen was not completed until a week before the conference was to open. Research materials to help familiarize delegates with the issues they will be discussing were not received by at least some delegates until last week.

The umbrella leadership group for organizations on aging has produced an ambitious "Eight for the Eighties" menu of fiscal and social programs to aid older Americans, including national health insurance and an expanded housing program. But given the lean look of the Reagan budget, it may be they will consider themselves victorious if they can mobilize the conference simply to oppose any further reductions in benefits for older Americans.