The executive committee of the Democratic Party voted yesterday to hold the party's third midterm mini-convention next June in Philadelphia's Civic Center. There was no controversy on the motion to stage the event there on the weekend of June 25-27.

Party Chairman Charles T. Manatt said the conference will come after many states have completed their primaries and serve to set the themes for the fall campaign. Reflecting growing Democratic optimism that President Reagan's economic plan will backfire before November, 1982, Congressional Campaign Committee Chairman Tony Coelho (D-Calif.) said, "I will stake my reputation that the Democrats will gain at least 10 seats" in the midterm House election.

The Philadelphia gathering will be smaller than those in Kansas City in 1974 and Memphis in 1978, with only 921 delegates. Some 364 of them will be the members of the Democratic National Committee, another 84 will be elected officials, 100 will be appointed by Manatt and almost all the remainder will be chosen by state Democratic committees.

Including DNC members and elected officials, the District of Columbia will have 11 delegates, Maryland 11, and Virginia 12.

Manatt used the executive committee meeting to unload some rhetoric against the Reagan administration, charging that "the Ronald Reagan high interest rate policy is bankrupting people and putting farms to the auctions and the sales blocks.

"Isn't it odd when Mrs. Reagan buys her china collection for $200,000 from as yet undisclosed private donors, and they the Reagan administration want grandmothers and widows over the age of 90 to have an assets test of $1,000," Manatt said.