DES MOINES, NOV. 15 -- Do not run a campaign that would embarrass your mother.

-- Sen. Robert Byrd's advice to Democratic candidates

A tearful Sen. Paul Simon announced his withdrawal from the 1988 presidential race this evening, following revelations that several of his aides had failed to wash their hands before a lemonade social and foreign-policy debate sponsored by a local elementary school PTA here last week.

This gaffe alone might not have been fatal, experts say. But the Iowa political community was alive with rumors that The New York Times was about to publish a story that the aides had not brushed their teeth afterward or written thank-you notes the next day. As Simon's staff's manners came to dominate the headlines, many Iowa Democrats became furious at Simon for diverting attention from President Reagan's recent announcement that intermediate-range nuclear missiles to be removed from Europe will be redeployed in Harlingen, Texas, and aimed at Nicaragua. What some experts see as a potentially valuable issue for the Democrats has now been overshadowed by the controversy over party etiquette.

Simon's departure leaves a gap in the Democratic field for 1988. Sen. Albert Gore Jr., Simon's only remaining rival, withdrew last week following revelations that his staff had leaked word that Rep. Richard Gephardt had cried upon learning that aides to the Rev. Jesse Jackson were responsible for informing the media that Gov. Bruce Babbitt's campaign had pointed the finger at Gov. Michael Dukakis' aides for revealing that Sen. Joe Biden had borrowed a speech from British Labor Party leader Neil Kinnock. Kinnock is expected to seize this sudden opportunity by announcing his candidacy tomorrow.

Political observers are divided over whether Simon's mistake was in not being aware of this social misbehavior on the part of his aides, in originally attempting to brush the issue aside, in hesitating for 15 minutes before firing the aides or in finally letting them go.

"In fact," explains William Schneider of the American Enterprise Institute, "it was all four. The voters will not excuse Simon from blame for his aides' performance simply because he didn't know about it. If a candidate cannot manage his own campaign, how can he manage the world's most demanding job? His original inclination to minimize this serious incident raises questions about his character. The delay while he vacillated about how to respond to this scandal naturally leads to concerns about his decisiveness. His final decision to let them go reveals an unseemly willingness to pander to outside pressure. What, after all, did they do that was so terrible?"

Schneider noted that the Reagan presidency has had a profound effect on the image a successful candidate must convey. "After eight years of Ronald Reagan's simple-minded bromides, the voters have come to expect leadership with a similar clarity of vision." He added, "After eight years of Ronald Reagan's hands-off management style, the voters have come to demand something completely different."

Some bitter Simon supporters are asking why the press should be focusing so much damaging attention on this episode, while a Republican candidate's recent strangling to death of his wife on national television has attracted relatively little notice. Media analyst Norman J. Ornstein explained: "He was already established in the public mind as a vicious character. His murder of his wife tells us nothing new about how he would perform as president. Simon, on the other hand, was perceived by the public as a clean and wholesome individual. Thus the revelation that those around him don't always wash their hands becomes a key element in assessing his character."

Simon aides also point to what they say is a lack of attention paid to acknowledgment by another leading Republican candidate that he diverted $15 million from the Iran-contra arms sale transaction to buy a chateau on the Loire for his French mistress.

"No, no, no," commented Marvin Kalb, director of the Harvard University Center for the Study of Politics, the Press, Policy Planning and Pepperoni Pizza. "That embezzlement was an isolated episode. Therefore, it is insignificant. Simon's hand-washing problems, however, highlighted concerns that close followers of politics already had expressed among themselves about a gravy-spotted shirt at a press conference last month and a poorly knotted bow tie during a candidate muffin bake-off and welfare symposium in New Hampshire last spring. Thus this episode confirms a pattern of behavior that raises legitimate questions about the candidate's character. I'm sorry, but those are the rules."

Another observer, who asked not to be identified, observed: "It couldn't just be that the press is unfairly picking on the Democrats, could it?" He added: "No, of course not. What on earth could I have been thinking of? Everybody knows the press has a liberal bias."