California strengthened its reputation as the "puzzle house on the Pacific" for the Carter administration today, as Vice President Mondale went through the kind of experience that seems to befall people only here.

He was heckled off a San Francisco stage by shouting "Gay Rights" demonstrators and was lobbied at breakfast by Gov. Edmund G. Brown Jr. - ordinarily a great critic of technology - for an expansion of the space program.

Then he flew into the smog of Los Angeles and proclaimed it, in an energy speech, a national model of a future "Solar City." And to cap it off, he appeared tonight at a Democratic Party fund-raiser with John Denver, the balladeer of simple outdoor pleasures, at a gaudy auditorium in - where else? - Universal City.

Despite these jarring moments, Mondale managed to proclaim a "healthy partnership" between the administration and Congress and to win from Brown some ungrudging praise for the "responsiveness" of the Carter administration to California problems.

The strange 24 hours began last night at the appropriately named Hall of Flowers in San Francisco's Golden Gate Park. Several dozen "Gay Rights" demonstrators had brought tickets for the $5-a-person Democratic fund-raiser, and a few minutes into Mondale's remarks they took up a chant of "Gay Rights Now."

Mondale immediately retired to the side of the stage, while California Democratic Chairman Bert Coffey and Mayor George Moscone pleaded with them to let Mondale finish.

The Vice President came back to the microphone to praise the administration's attack on unemployment and its human rights campaign, but when the chant began, "Gay Rights Are Human Rights," Mondale declared his part of the meeting finished. He left several hundred party supporters with hands unshaken and headed downtown for dinner so abruptly that when Sen. Alan Cranston (D-Calif.) arrived he found the stage had been taken over by homosexual dancers.

This morning at breakfast, Brown lobbied Mondale for closer cooperation on water problems, cautioned against "any dramatic increase" in nuclear power plants, and - surprisingly - put in a strong plug for more spending on space.

Brown has portrayed himself as an enemy of runaway technology, but the aerospace industry is one of California's chief businesses. He told reporters he had tried to persuade the Vice President that he space shuttle (built in California) "is like the last spike in the transcontinental railroad" in terms of its importance for America.

After breakfast, the governor, who is viewed by the White House as a potential Carter challenger in the 1980 Democratic primaries, joined Mondale at a brunch for big contributors, telling them, "It's a great thing when the administration in Washington is sensitive to the problems of California."

Brown hitched a ride to Los Angeles on Mondale's plane, but then ducked out of sight. He told reporters, "We've got people from Washington coming out here every day, and you can't be with them constantly."

Mondale addressed an energy conference of the National Democratic Forum, making no reference to administration defeats in Congress on gasoline taxes, but saying he and Carter were "deeply disappointed" at the House subcommittee vote to decontrol natural gas prices. "We hope and expect the Congress to reverse that action," he said.