At appropriate moments, this column has commented that whatever the deficiencies of the American system of government, it works better than anything else that has been tried.

At times, however, one has cause to wonder whether the system works at all, let alone works well.

Consider last week's news flow. On Monday we learned that the wealthiest 5 percent of the nation's taxpayers get almost half of the $84 billion worth of special tax benefits that Congress has written into our tax laws.

On Monday we also read the latest on the attempts of Chief Justice Warren E. Burger to upgrade the quality of legal representation in our courts, and also the latest on the bitter opposition he is getting from the legal profession. Burger says almost half the lawyers who appear in court are incompetent, and the lawyers say this is an exaggeration; the percentage of incompetents may be no more than one-third.

Tuesday's paper told us that 2.5 million tons of coal have been exported from this country since the start of the coal strike. Wednesday we read that H.R. Haldeman is bringing out his own version of the history of the Nixon years and Watergate. Everything at breakfast tasted stale and sour Wednesday.

Thursday the good word came from the New York Court of Appeals, which handed down a decision in a domestic relations case that involved alimony. Ordinarily, an order to pay alimony remains in effect until it is terminated by death or the woman's remarriage. The rationale appears to be that so long as a divorced woman has no other means of support, her former husband is stuck with that responsibility. But if she remarries, her new husband is expected to support her.

In 1938, New York modernized its laws and decreed that a man could stop paying alimony if his former wife began living with another man, even without benefit of clergy, and held herself out to be his wife.

In the case being considered, the wife hadn't remarried, but had simply moved in with another guy. So the husband stopped paying alimony, and the wife took him to court. The Court of Appeals, in its wisdom, ruled that the alimony had to continue. Why? The woman hadn't represented herself to be the new boyfriend's wife. She hadn't applied for any bank accounts or charge accounts as his "Mrs." She was just shacked up with him, and what's wrong with that, for heaven's sake? Pay up, sucker.

The House of Representatives' investigation of itself in the Korean influence-buying scandal moved along with all the speed and vigor one can expect of a self-investigation. On Friday of last week Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) gave us a new definition of chutzpah.

Secret testimony that Korean manipulator Tongsun Park had used O'Neill's office as a hangout triggered an angry response from the distinguished gentleman from Massachusetts. He entered his attention not on the charges, nor even on a denial of them, but on what veteran staff writer Richard L. Lyons termed "an extraordinary personal attack" on Rep. Bruce Caputo (R-N.Y.), whom O'Neill accused of making the secret testimony public.

The transgression, as you can see, is not in doing the deed but in letting the public know it was done.

Saturday's paper brought word that in 1975 there had been a grand jury investigation into the letting of Montgomery County contracts, and that it had turned up evidence of conflict of interest, "money changing hands," chaotic record keeping, bungling and mismanagement. "The employes involved were never prosecuted."

Yesterday's paper is still too fresh in our minds to need much review.

In its 75th day, the coal strike stood where it stood on its first day.

W.A. (Tony) Boyle was, for the second time, found guilty of ordering the assassination of his union rival, Joseph (Jock) Jablonski in 1969. Now, 8 years later, the verdict will be appealed again and the case will drag on.

In 1964, the United Auto Workers began trying to get a labor contract with Monroe Auto Equipment Co. In 1966, the UAW at Monroe won an election supervised by the National Labor Relations Board. But appeals and other legal maneuvers occupied the next 12 years. It wasn't until last week that the union got its contract.

Even Friday night's "4 to 7 inches of snow" failed to materialize and the standard joke was, "It must be coming by parcel post." It just wasn't a very good week for those of us who think the system works well - most of the time.