The American Postal Workers Union convention doesn't open until this morning, but it is already off to a rocky start. Hundreds of arriving delegates already have announced they will vote against the tentative contract their leaders have signed with the U.S. Postal Service. Some are carrying newspaper articles quoting AFL-CIO president George Meany as saying it "isn't a very good" contract.

As if they did not have enough troubles with the contract and their attempts to head off a strike, union leaders are also contending with a very serious, very human problem. Some delegates have arrived nearly broke, or low on funds, because U.S. Postal Service computers short-changed them in their last paychecks, or did not issue any checks at all.

The computers that crank out bi-weekly paychecks for more than half a million postal workers have been acting up for the past three months. But the last payroll - the one just before this convention - was the biggest problem. That's because workers already are mad at Jimmy Carter, the Postal Service, their leadership or all three. Many of them have come here to do something about it. "The paycheck foul-up this time is just the last straw," a New York delegate said. He said he wasn't personally caught up in the payroll snafu, but hundreds of his members are, and "I'm taking gas from them. And believe me, I'm gonna pass it on to somebody."

APWU president Emmet Andrews got wind of the gas last week during a pre-convention meeting of the union's executive board here. "I called (Postmaster General William) Bolger personally and told him "you aren't helping me any.'" Andrews said the Postmaster General assured him that all regular employes would be paid their salaries - through special check or advance - without question. Nevertheless, the continuing computer foul-up could not have come at a worse time for the union, its members, or the Postal Service.

The union president and the postmaster general have several problems in common. Bolger is taking heat for agreeing to continue the "no-layoff" pledge in the new three-year contract. Postal officials want to reduce the work force, but will not be able to get rid of excess employes - except through attrition - because of the life-of-the-contract job tenure. Bolger wants to avoid a postal strike, realizing that a long one could wreck the government corporation that now handles the mail and could cause Congress to eliminate the government monopoly on delivering first class mail.

Andrews, along with two other top AFL-CIO postal union leaders, have signed the new contract, subject to a referendum vote of the membership. The phased-in 19.5 percent pay package has disappointed many employes. Militant local union leaders in Pittsburgh, New York, Philadelphia and on the West Coast are calling for a strike. Two weeks ago Letter Carriers Union president Joseph Vacca ran into a heavy anti-contract storm at his Chicago convention. At one point delegates booed and jeered Vacca several minutes when he mentioned the contract.

The postal union leaders have another serious problem from an unexpected source. AFL-CIO president Meany's downgrading of the wage portion of the contract has hurt union leaders who are trying to convince members it is the best under the circumstances. Postal wages and fringes consume eight cents of every dime the USPS makes. Pay raises tend to trigger politically unpopular stamp price increases. Winning the no-payoff clause - a benefit almost unheard of in industry - is worth a lot of money, the leaders think. The question is whether they can convince delegates here of the value of lifetime tenure, or whether the delegates return home to their cities and recommend a strike.

The U.S. Postal Service and the Tennessee Valley Authority are the most heavily organized government activities. Nearly 90 percent of the Service's 550,000 rank and file employes belong to unions.

APWU is the biggest of the postal groups with around 220,000 dues paying members. Its president and other national officers will be elected in a one member one vote mail ballot in early September. Their jobs and the likelihood of a strike depend heavily on how smoothly this week long convention functions.