When Dan Quayle was tapped for the No. 2 spot on the Republican presidential ticket, the U.S. senator from Indiana was plucked from relative obscurity and suddenly shoved into the national spotlight.

Because the American public was largely unfamiliar with him, a useful and legitimate purpose was served by efforts to delve into Quayle's background in public service and private life.But there is a point at which a serious inquiry can start turning into a snide inquisition. That point seems to have been reached and exceeded with the repeated harping on the fact that Quayle was able to enter a National Guard unit that stayed in Indiana during the Vietnam war.

The drumbeat persists even though the public is now being told little, if anything, about this episode that wasn't disclosed during the Republican National Convention or shortly after.

This constant hectoring of Quayle is hard to understand except as an exercise in either sensation-mongering or political hypocrisy.

Are we really to believe that the American people should be outraged by something that didn't bother the voters of Indiana when they elected Quayle to two terms in the U.S. House of Representatives and two in the U.S. Senate?

Are we to believe that those who keep picking at this situation to the neglect of other campaign issues have better judgment and superior moral values?

That must come as news to the 74 percent of Americans who, in a recent Newsweek poll, said they aren't bothered by Quayle's National Guard service.

Or is it that service in the National Guard or Reserves during wartime disqualifies one only for the top jobs in the executive branch of government but not for the legislative branch?

If so, that must come as news to the House and Senate members who, like Quayle, have also served in the National Guard. It must also come as news to the 203 lawmakers of the same age group that could have served during the Vietnam war but remained out of any military branch. Must many of them forget about any presidential or vice presidential ambitions?

What about the accusation that Quayle displayed hypocrisy in avoiding combat 19 years ago but voting repeatedly in Congress for a strong military stance now? How many of Quayle's accusers - or anyone else, for that matter - would care to be judged forever on the basis of decisions and events that took place decades ago?

Or is the incessant harping on the National Guard episode just a backhanded way of maintaining that Quayle is too much of a "lightweight" to become vice president, let alone possibly succeed to the presidency?

If so, keep in mind that, at 41 years of age, Quayle is almost as old as John Kennedy was when Kennedy ran for the White House, has served as long in Congress as Kennedy did, and has a legislative record at least as impressive as Kennedy's. On Inauguration Day, Quayle will be just six months younger than Teddy Roosevelt was when he became vice president.

In any event, volumes are being written and spoken about an episode that deserves to be only a footnote in the 1988 election campaign. There are sharp limits to how much longer the press and various politicians can keep harping on this theme without creating a backlash of sympathy for Quayle and antagonizing the millions of Americans who have served in the National Guard over the years.

Now that this and other aspects of Dan Quayle's life have been thoroughly explored, it's time to move beyond such side-issues and start focusing on the key parts of the Bush-Duakakis presidential contest.