Both vice presidential nominees can find good news in a poll conducted by the Gallup Organization for the Times Mirror Co.

Sen. Lloyd Bentsen, D-Texas, was regarded by far greater numbers of registered voters than Sen. Dan Quayle, R-Ind., as qualified to serve as president, if that became necessary.On the other hand, an overwhelming majority of the 1,000 people contacted nationwide by telephone Wednesday and Thursday said that they think no less of Quayle because he chose to serve in the National Guard during the Vietnam War.

Moreover, a large majority said that they would not hold a less favorable opinion of Quayle if they learned that he had used family influence to join the Guard to avoid being drafted.

Also, large majorities said that they believe that news coverage of Quayle, following his selection as GOP presidential nominee George Bush's running mate, has been too extensive and unfair.

The survey also found that both Bush and Michael S. Dukakis, the Democratic presidential nominee, continue to gain in the number of voters who view them favorably, but their similarly high ratings are still topped by the present White House occupant, Ronald Reagan.

In what is becoming a major campaign issue, 62 percent found Bentsen qualified to step in as president, while 16 percent said that he was not qualified. Opinion on Quayle divided evenly: 41 percent said qualified, 40 percent said not qualified. The remainder in both cases said that they did not know.

Quayle has been beset by news stories about how and why he joined the National Guard in 1969, a move that greatly reduced his chances of being sent into combat. In the survey of voters, 82 percent said that they did not have a less favorable opinion of Quayle because he chose the Guard. A smaller, but still considerable, majority - 63 percent - said they were not bothered by questions of whether Quayle had used family influence to get into the Guard. (Records released Friday indicated that the Guard had vacancies and such influence was not needed.)

At the same time, 69 percent believed that there was too much news coverage of Quayle's past, which included not only the Guard matter but uncorroborated allegations that he had propositioned a female lobbyist while on a 1980 golfing trip with two other congressmen in Florida.

Also, 55 percent of the registered voters said that news organizations had been unfair to Quayle. However, 56 percent said that it was important that voters learn about the details of Quayle's past in order to judge whether he would be a good vice president; 38 percent said that such details were not related to his ability to serve in the post.

Surprisingly, those polled said that they followed three other stories more closely than the Quayle imbroglio - the farm drought, the downing of an Iranian passenger plane by a U.S. Navy ship and the hot weather.

Meanwhile, 65 percent said that they were very or mostly favorable about Bush, a gain of 5 percentage points from a week earlier, at the end of the Republican National Convention.

Dukakis' rating rose to 59 percent, an increase of 4 points during the same period.

President Reagan, who had a 67 percent favorability rating, continued to outpace them both.

Quayle's favorablity was 50 percent, Bentsen's 48 percent.

Those surveyed rated Bush and Dukakis about even on ability to get things done, make good decisions and use good judgment. However, Dukakis was given an edge on being concerned about people's needs and being strong and forceful.

The margin of error for the survey was plus or minus 3 percentage points.