The continuing resolution signed by President Reagan yesterday provides funds for a wide array of arts activities locally and nationally, including an estimated $250,000 for the President's Committee on the Arts and Humanities, $15 million to rebuild the Filene Center at Wolf Trap and a $1 million bonus for the National Symphony Orchestra.

Budgets for the National Endowments for the Arts and Humanities remained virtually unchanged from last year's levels.

The catchall spending bill rushed through Congress Monday night and signed by the president at 1:51 p.m. yesterday explicitly authorizes the arts endowment to fund the star-studded presidential Committee on the Arts and Humanities, which seeks to increase private support of the arts and humanities. A House version of the bill, sponsored by Rep. Sidney Yates (D-Ill.), had sought to kill the committee's funding.

"He did indeed try to ax it and would have gotten it axed if I hadn't insisted it be funded," said Sen. James A. McClure (R-Idaho), who chairs the Senate appropriations subcommittee that deals with the arts and humanities and who chaired the House-Senate conference committee that dealt with these matters prior to Monday night's votes.

McClure said the committee, which includes singer Frank Sinatra, Reagan "kitchen cabinet" member Armand Deutsch and former Time Inc. Chairman Andrew Heiskell, "can provide a useful function, and that's particularly true as we're looking toward greater private participation and funding in the arts and humanities . . . I guess it would be fair to say, too, that the first lady wants it very badly and . . . she urged me to reinstate it."

With yesterday's action, between $175,000 and $250,000 in money from the arts endowment is expected to go to pay the committee's administrative costs, although officials said the figure could go higher.

While the National Symphony Orchestra will receive its one-time grant for its role as "the resident orchestra of the Kennedy Center," the Washington Opera was a big loser yesterday. The Senate version of the bill had included a $1 million grant for the opera, to be given on a matching basis, but the funds were killed in conference.

"We lost out on a million bucks we didn't have," said Martin Feinstein, the opera's general director. "It would have helped our deficit situation enormously, but we realize that things that go on in Congress are uncertainties and you cannot count on them."

Feinstein said the opera was $730,000 in debt but hoped to be in the black within three or four years.

The money for Wolf Trap includes $7 million that was remaining to be appropriated on a $9 million grant, plus an $8 million loan. The Filene Center burned down last April, with no insurance to pay for rebuilding.

Wolf Trap Executive Director Ed Mattos said the action by Congress and the president was "a testimony to the contribution to Wolf Trap that we want to go on making, and we're grateful. We're going to work hard . . . to pay the $8 million loan back. We think there's a debt of honor involved and a debt of confidence."

The $143,875,000 appropriated yesterday for the arts endowment is 43 percent more than President Reagan originally requested, and it was the figure in both the House and Senate versions of the bill.

The humanities endowment will receive $130,060,000, about 35 percent more than the president had originally requested. The House version had had an additional $500,000 for administration, but the House conferees agreed to the Senate version's lower number.

The national endowments are the federal government channels for subsidizing the arts and humanities.

The bill signed yesterday also appropriates:

* $250,000 on a matching basis for the National Symphony Orchestra to perform a Fourth of July Concert on Capitol Hill and have it televised. This event was also funded in 1981 but not this past last July 4.

* $10.8 million for the Institute of Museum Services, a federal office that gives grants to museums around the country and that the administration didn't want funded at all.

* $32,878,000 for the National Gallery of Art. The figure represents about a $400,000 increase over last year's funding figure, according to J. Carter Brown, the National Gallery's director. However, Brown said the gallery's operating budget -- for special exhibitions and salaries, among other things -- was cut in the action by about $400,000, with more of the total budget going into the gallery's long-range renovation program.

"I guess it's good news and bad news," Brown said. "We're sad on the operating front and we're happy on the construction because we think that's a wise move in terms of saving the government money in the long run."