Dallas — As Walter Mondale struggles to restart his distracted campaign, the Republicans leave this sweltering city feeling that they are on a roll. To no one's surprise, they accomplished what they set out to do: stage an orderly, crisp, upbeat national convention that projected a party buoyantly unified around its standard-bearer and eager to work for a rousing victory in the fall election.
Riding a crest in his popularity, President Reagan is proclaiming that the Republicans are ''America's party for the future,'' and he's sounding the themes of ''opportunity'' for all Americans and ''an expanding economy'' under Republican rule.
Mr. Reagan is taking on the Democrats with partisan glee. Americans have a clear choice, he says, between the ''great-opportunity party'' and the Democrats , with their ''worn-out, discredited, far-left ideology that caters to special interests.''
Religious values will continue to be central in Reagan's campaign. Addressing critics who say that he has promoted policies that break down the wall of separation between church and state, Reagan says his administration will never establish any religion in violation of the First Amendment.
But he said at an ecumenical prayer breakfast Thursday: ''The truth is, politics and morality are inseparable - and as morality's foundation is religion , religion and politics are necessarily related. We need religion as a guide. We need it because we are imperfect and our government needs the church; because only those humble enough to admit they're sinners can bring to democracy the tolerance it requires in order to survive.''
Delegates were jubilant over the convention.
''We've got to get out there and pull the vote in,'' said Marion Crecco, a delegate from Bloomfield, N.J. ''Too many people think Reagan's got an easy shot.''
''I've never seen a more unified, enthusiastic group than here,'' commented Mayor Elmer Conti of Elmwood Park, Ill. ''But Republicans have been too complacent. When people are happy, they stay home and don't vote. The Democrats are mad and will be there on Nov. 6. So we have to reemphasize what's happened in the last four years.''
Preaching a message of national uplift vs. Democratic ''defeatism,'' Reagan now plunges into the campaign looking to have every advantage in the election race. The economic recovery continues to blunt Democratic attacks on his administration. Polls show him running ahead in virtually every region of the country. Republican coffers are full. Not least of all, Mr. Mondale has lost valuable time - and perhaps ground - because of the difficulties surrounding his running mate.
But despite the well-scripted GOP convention, which many feel was not all that important in any case, there are factors that political experts say should be kept in mind as the nation looks ahead to the election:
* Republicans remain the minority party and are therefore working from a smaller base than the Democrats. For all the convention calls to Democrats to ''come on over,'' Reagan strategists are conscious that 40 percent of Americans call themselves Democrats, while only 25 percent or so identify with the Republican Party.
Moreover, as the convention showed, the Republican Party has internal strains , and hangs together largely because of the figure of Ronald Reagan.
Underlying the convention was a ''sense of tremor'' about what would happen if Reagan was not reelected or was weakened by 1986, says Washington political analyst Norman Ornstein. ''Eisenhower also was a popular figure and won a big victory in 1956, but by 1958 the Republicans suffered a resounding defeat (in congressional races).
''The Republicans, in short, rise and fall with Reagan.''
* The GOP also has some issue problems. The hard-line conservative platform adopted at this convention is out of step with mainstream Republicans, analysts say, and is to the right of the majority of Americans.
Most Republicans, for instance, are conservative on economic issues but take exception to the party position on abortion, women's rights, and other social issues.
They also support a nuclear freeze, and Ronald Reagan has been plagued since he came into office with the image of being a warmonger. Democrats will seek to reinforce that image - by playing up his recent joke about bombing the Soviet Union, for instance, as a sign of the ''real Reagan.''
''An interesting aspect of the campaign will be the relation of the radical right to the campaign and the administration,'' says presidential scholar James Barber. ''The right has been tossed a bone, but the relationship between the Wall Street Republicans and the conservative right is tense.''
* An incumbent president has to worry about whether the present realities of the world will hold enough to work to his advantage. If the economy slips, if some untoward international event takes place, the Republicans could find themselves suddenly on the defensive.
* Americans have not yet fully made up their minds about the Reagan-Mondale race. (Estimates of ''undecided'' voters range from 10 percent to 30 percent.)
Democrats obtained a temporary boost in the polls after San Francisco. The Republicans are expected to do the same now. But these horse-race soundings have to do more with the preoccupation of political strategists and news media than with a true reflection of opinion on Election Day, experts say.
''The majority of Americans don't focus until after Labor Day,'' says Dr. Ornstein. ''They may look at Mondale in the abstract, but the volatility in the polls shows they will not start to compare the two men (until after Labor Day), and events will determine what happens.''
Still, the Reagan position at the moment looks strong. Although the Republicans are a minority, experts point out that since 1960 the Republicans have been able to command equal support in presidential races.
Much of the electoral vote already looks secure for Reagan. Conservative Democratic analyst Horace Busby has written that with few exceptions, states west of the Mississippi have voted 6, 7, or 8 times for the Republican candidate in the past eight elections. So that region is basically no longer a battleground.
''That means the Republicans can pay less attention to that area and concentrate on Texas, Ohio, Illinois, and other areas of potential strength for the Democrats,'' says political scientist Thomas Cronin. ''The Democrats have very few states they can count on.''
The unknown question now is the effect of the Ferraro financial issue and whether Mondale can put it behind and get on to the general election campaign. If he can, say experts, and especially if debates with the President are held, he may be able to show that he has a reasonable alternative.
Republicans, in any case, leave for home happy and energized. ''When I came I was tired of politics,'' remarked Lois DeVecchio, a delegate from Washington, D.C. ''Now I'm rejuvenated!''