A vitriolic and improbable dispute has suddenly erupted between the Palestine Liberation Organization and Col. Muammar Qaddafi, the unpredictable Libyan leader who previously was among the PLO's staunchest supporters.

The quarrel has Palestinian officials here calling Qaddafi a "madman" and making impolite reference to his Bedouin upbringing. It has Qaddafi accusing the PLO of betraying the Palestinian people and comparing PLO leader Yasser Arafat to Prime Minister Menachem Begin of Israel.

The explosion of insults has blasted a large and highly visible crack in the Arab front ranged against Egyptian President Anwar Sadat's peace policies, joining the feud between Syria and Iraq as an obstacle to effective Arab action against Sadat.

In addition it has raised the prospect of a fund cutoff for radical Libyan-backed guerrilla groups under the PLO umbrella.

In some ways, the name-calling is a classic example of the intra-Arab bickering that often erupts out of nowhere for obscure reasons and then just as suddenly passes from the Middle East landscape in a fraternal reconciliation replete with kisses on the cheek.

Yet under the surface, it also is a new illustration of the opposition Arafat has encountered in his effort to steer the PLO toward moderation and diplomacy rather than guerrilla raids in the battle against Israel.

Qaddafi repeatedly has urged the Paletinians to follow a more bellicose line against the Jewish state. Libyan funds traditionally have been a major source of income for extremist Palestinian groups that advocate terrorism within Israel and outside as a legitimate Palestinian tactic.

Earlier this month, Qaddafi called on the PLO to attack oil fields from which Israel gets petroleum and to blow up ships to block the Suez Canal as retaliation for Sadat's peace treaty with Israel. In so doing, he implied that Arafat was abandoning armed struggle against Israel.

Arafat's command here regarded this as little more than another example of the bluster for which Quaddafi has become known since he took over in a bloodless military coup in 1969. Similarly, the PLO leadership dismissed Qadaffi's declaration that the approximately 40,000 Palestinians in Libya should form "popular committees" to supplant regular PLO structures here.

According to Palestinian sources here, however, Qaddafi this time apparently was determined to get some action. Why he decided to act now remains a mystery even to informed Palestinians. But guerrilla officials point out that Arafat and the Libyan leader had been on bad terms for several months, among other things because Qaddafi refused to channel Libya's payments to Palestinian groups through the central PLO exchequer run by Arafat.

"He has not paid us one stinking dinar since 1974," shouted one PLO informant, shaking his finger angrily. "Not a thing to Fatah, to the PLO, to the Martyrs Fund [for families of slain guerrillas], not even to the damn Palestinian Red Crescent."

Instead Qaddafi's funds have gone directly to the more radical Palestinian groups, including the Popular Front for the Liberation of Palestine of George Habash, the Democratic Front for the Liberation of Palestine of Nayef Hawatmeh, the Palestine Liberation Front of Abul Abbas and the Popular Front for the Liberation of Palestine -- General Command of Ahmed Jibril.

The independent funding strengthened these forces against Arafat in a debate over his recent attempts to portray the PLO as a responsible political organization and worthy interlocutor for talks on the future of the West Bank and Gaza. This internal discord, muted since the Camp David accords, had become more obvious in recent weeks as various PLO leaders argued over how best to deal with the Iranian revolution.

Against this background, Palestinian officials here say, some Palestinians in Libya heeded Qaddafi's call and formed popular committees in open challenge to the chief PLO representative there, Suleiman Shurafa, also known as Abu Tariq.

At this point Arafat's command apparently decided the dispute was getting out of hand and dispatched to Tripoli a peace-making delegation composed of Palestinians from the PLO groups most closely aligned with Qaddafi.

Palestinians here say the delegation was well received and Libyan officials intimated they, too, wanted to dampen the disagreement. Delegation members report that when they returned to Beirut Monday night they thought the quarrel was on the way to resolution. The next day, however, Qaddafi told Western reporters in Libya that he had expelled Abu Tariq because he was extorting money from Palestinians in Tripoli and "even tortured some of his compatriots."

"After what I witnessed from Fatah in the last few days, I realized why those Lebanese who were exposed to unbearable provocations chose to become allies of the Israeli enemy rather than allies of Fatah," he told Agence France-Presse.

"I also was able to understand why the Syrian Army hit them and then entered Lebanon, why the Iraqi government fought against Fatah and why King Hussein evicted them from Jordan."

Enraged and feeling betrayed, radical guerrilla leaders joined Arafat's mainline command in a PLO Executive Committee communique sharply criticizing Qaddafi and restoring the quarrel to the front pages of Beirut newspapers. The tenor of Qaddafi's comments seemed to serve as a temporary rallying point for Palestinians of all tendencies, including those who rely on Qaddafi for funding.

When he heard of Qaddafi's remarks, a Popular Front official fumed, "What is he doing, the madman? Doesn't he realize that if it comes to a choice between him and Arafat, we will always choose Arafat?"