San Francisco — Striking copper miners bused in from Arizona to march in labor demonstrations , 100,000 homosexual-rights activists marching on Moscone Center, the lone but determined Jesse Jackson delegate from Oregon, the party boss struggling to keep his job - at every level the Democrats have a tough job maintaining a unified face here this week.
The liberal agenda is to beat President Reagan. But that goal often is the only common denominator among the Democratic factions, whose back-room caucuses and street demonstrations constitute a brew that the party leadership hopes to keep from boiling over onto the convention floor and into the national spotlight.
Interviews with representatives of special-interest groups suggest that Walter Mondale's selection of Rep. Geraldine A. Ferraro as his running mate initially has built a feeling of party solidarity among minority delegates. They say they are optimistic that the break with tradition will ultimately open doors for Hispanics, blacks, Asians, homosexuals, and more women.
There have been daily demonstrations on the streets here since the weekend, but most - including the 100,000 homosexual marchers and the 100,000 labor union marchers - have been shows of support for the party and a bid for national publicity on the various issues.
The labor rally was ''no protest at all, but a show of the strength of labor, '' explained Richard Trumka, president of the United Mine Workers International. And the homosexual-rights rally, said homosexual convention delegates, similarly was a show of support for the Democratic platform, which opposes discrimination against homosexuals in housing and employment.
A variety of other groups, like the nuclear freeze advocates and anti-hunger and pro-marijuana groups who staged rallies here, hope to push their causes with delegates.
But, says Ed Costantini, a political science professor at the University of California at Davis and a veteran of several Democratic conventions, the system does not allow for these groups to change anything now. Major grievances, he says, could make it to the convention floor, but ''most special interests have had their say in the platform hearings (months ago).''
Special-interest caucuses, such as labor, environment, women, and minorities, say their job during the convention and through the November elections is to push to maintain support for the ground gained in platform planks on their particular issues. Except for the signs carried on the convention floor by delegates, this caucusing is not a process that will be visible to Americans viewing the convention on television.
Some differences over platform issues will be exposed for everyone to see when four minority planks are debated - the only scheduled debate on the convention floor. Jesse Jackson supporters have raised four issues for debate - only three of which now will actually be pursued: reducing military spending, strengthening party positions on the Voting Rights Act, and a ''no first use'' nuclear arms policy. The fourth issue for debate is Gary Hart's minority report, which outlines when a Democratic president should not use military force. Jackson also raised the issue of affirmative-action quotas, but that won't be debated on the floor.
One dispute that could indirectly find its way to the convention floor is Hispanic discontent over congressional passage of the Simpson-Mazzoli bill - an immigration reform package including a guest-worker program and employer sanctions opposed by Hispanics but passed with the help of many Democrats.
A first-ballot boycott over the issue is being pushed by Mario Obledo, president of the League of United Latin American Citizens, the nation's largest Hispanic organization. The boycott would act as a sanction against the Democratic establishment, which didn't oppose the bill strongly enough, Mr. Obledo says.
But most elected Hispanic officials here oppose the idea.
''The real concern is how the Democrats responded to the issue. It was the Democrats that passed it,'' says Gov. Toney Anaya (D) of New Mexico, referring to the fact that the Simpson-Mazzoli bill could not have passed without Democratic support.
''But a boycott would seem to be a direct attack on Mondale,'' because 60 percent of the Hispanic delegates are pledged to Mondale, concludes Governor Anaya, leader of the New Mexico delegation. He says he'll discourage the boycott.
But, he adds, most Hispanic delegates will want to be heard on the question, perhaps by submitting an amendment to make platform language on immigration oppose the whole Simpson-Mazzoli bill, rather than the present wording, which singles out only certain objections.