Finding common ground in opposition to the government's strike-ending efforts, the coal industry and United Mine Workers resumed face-to-face bargaining yesterday in hopes of reaching a negotiated settlement this weekend.

In a bizarre turn of events, the Carter administration's double-barreled drive to get some miners back to work under the Taft-Hartley Act and to encourage some companies to settle separately or regionally had a decidedly different effect.

By exposing both sides to the mutually threatening prospect of Balkanization of labor relations in the coalfields, the administration's tactics apparently served as a catalyst to end the government-declared impasse in industrywide bargaining.

Company-by-company or regional settlements might get some coal moving again to relieve electric power shortages in eastern and midwestern states, thus easing political pressure on the White House for action. But such settlements could break up the industry's united bargaining front and further shatter the strife-riddled UMW, giving the national leaders of both groups common cause to unite against the government.

Hence, face-to-face talks were resumed for the first time in two weeks in an atmosphere of some optimism on both sides, although there was no assurance that the new bargaining would succeed.

Meanwhile, the government contributed to coalfield confusion on two other fronts yesterday:

The Justice Department accidentally omitted copies of a court summons from legal papers that federal marshals will be delivering over the weekend to 1,450 UMW and industry officials so that a temporary back-to-work order can be enforced starting Monday afternoon.

Copies of the one-page document, which calls for aresponse to the government's petition for an 80-day injunction against striking, were being rushed to the coalfields by couriers yesterday after the omission was detected. A back-to-work order cannot be enforced before the summons is served, department officials conceded.

Agriculture Secretary Bob Bergland said he was instructed local welfare offices to deny food stamps to miners who defy the Teft-Hartley order but acknowledged that his legal authority to do so is unclear. "I've issued a notice of my intention to enforce a regulation that is not clearly legal," said Bergland. "If I'm hauled to court, it may be necessary to preent the Congress with a proposal to change the law."

Although federal law permits strikers to receive food stamps, which average about $25 per person a month, a departmental regulation denies them in the case of an illegal strike. According to a Library of Congress analysis, this regulation was declared illegal by a federal court in California two years ago and is thus open to legal challenge.

The coal negotiators' return to the bargaining table apparently came as a surprise to the administration, which was still talking of an impasse and separate settlements late Thursday while top company and union officials were meeting privately to plan the resumption of industrywide bargaining.

"The effort to get a breakoff obviously triggered a resumption," said one bemused and admittedly bewildered administration official.

"What you have here," said an industry source, "is a strong mutual desire to keep the government out."

Said UMW President Arnold Miller as he prepared to meet again with industry negotiators: "If it's going to be resolved, this is where it's going to be resolved . . . not by any intervention."

As both sides gathered shortly after 10 a.m. around a large table in a Capitol HIlton Hotel suite, smiling for the benefit of photographers, there was no guarantee that this latest round of talks would bring an agreement - or that an agreement could be sold to the 160,000 strikers, who last weekend overwhelmingly rejected a contract that had been negotiated under White House pressure.

The rejected contract provided a 37 percent increase in wages and benefits over three years but included wildcat strike curbs, pension inequities and drastic changes in health care, including benefit deductibles, that most miners found unacceptable.

Agreement by the Bituminous Coal Operators Association to resume bargaining indicated the industry may be willing to make significant concessions on some or all of these points. The union was believed to have less flexibility, because of the lopsided rank-and-file rejection of the earlier contract offer.

One industry source spoke of a "psychological advantage" in reaching a tentative settlement before the government on Monday starts enforcing the Taft-Hartley back-to-work order, which many miners have vowed to ignore. Similarly, speedy rank-and-file ratification might obviate the need for the full 80-day injunction. A hearing on the injunction has been scheduled for next Friday.

Shortly before bargaining recessed for the night, UMW officials said telegrams have been sent to all union district and local units ordering them to instruct members to "cease their strike activity and return to their normal place of employment." The order, approved earlier in the day by the UMW's national officers and executive board, was designed to meet Taft-Hartley requirements for union compliance with an injunction.

There was no word on the substance of yesterday's talks, but Miller told reporters that no contract would be acceptable to miners unless it included full restoration of health benefits. The rejected contract called for guaranteed benefit payments but would have imposed deductibles of up to $700 a year per family for medical care, which was previously free but subject to cancellation when wildcat strikes and other work stoppages cut production royalties.

Yesterday's talks were conducted without any government mediation efforts, although mediators helped set up the talks. Labor Secretary Ray Marshall mediated the last round of talks but was not invited to participate yesterday.

Industry bargainers included key figures from several of the biggest coal companies: Peabody, Pittston, Island Creek and Consolidation. Some of these had figured in earlier speculation about possible breakaway settlements.