U.N. Secretary General Kurt Waldheim dispensed bland optimism here yesterday during a visit that failed to clarify major areas in what could become the world organization's most perilous peacekeeping mission to date.

During a seven-hour stopover - in which he conferred with Palestinian commander Yasser Arafat, President Elias Sarkis and other Lebanese officials - Waldheim failed to break new ground.

For the record, he reiterated his demand that Israel speed up its withdrawal from southern Lebanon in compliance a Security Council resolution, adopted a month ago, demanding a pullout "forthwith." He made it clear that the U.N. peacekeeping force would not take on any new mission outside the territory occupied by Israeli troops in last month's invasion.

Only about 2,500 men of the peacekeeping mission's presently authorized strength of 4,000 are now deployed and Waldheim did not expect all the assigned troops to be here for another two weeks.

In addition to the slowness of deployment, the United Nations faces other problems here: the weakness of the Lebanese army, the doubtfulness of Palestinian cooperation, the continued Palestinian presence north of the area occupied by Israel, and the issue of what to do about Israel's policy of supplying Christian Lebanese forces across its border.

Until the troops are at full strength, diplomats are convinced that the Israelis will not withdraw much beyond the territory they have already handed over to the United Nations - about one-tenth of the 450 square miles they occupied.

In the past few weeks, both the Israeli and Lebanese governments are known to have pressed the United Nations to move north of the Litani River.

Lebanese Christian warlords, in fact, want the United Nations to take over all peacekeeping chores in Lebanon, replacing the 30,000-man Arab deterrent force, mainly made up of Syrians, now policing the rest of the country.

As articulated by Dory Chamoun, secretary general of the National Liberal Party, only a U.N. force can provide the "neutral non-Arab army" needed to bring the Palestinians to heel while the fledling Lebanese army is being trained and deployed.

For Chamoun and many other Christians, the United States bears the major responsibility for ensuring that such a U.N. force is dispatched to Lebanon.

They affect disbelief when told that the Soviet Union would veto such a plan.

Other problems facing the United Nation are more tangible.

Part of Security Council Resolution 425 approving the Peacekeeping force also called on Lebanese army units to serve alongside the U.N. troops in helping restore Lebanese authority in the south.

But the Lebanese army does not exist as anything approaching a fighting force. At least four to six months are generally thought necessary to field any such Lebanese force military analysts say even wildly optimistic.

Despite Palestinian leader Arafat's reported assurances that his forces would cooperate with the U.N. forces, serious doubts persist in only because of ill-defined relationships between the guerrillas and the peacekeeping mission.

The Palestinians are willing to further U.N. efforts to expedite the Israeli withdrawal, but they are unwilling to give up any position they occupied at the time Israel declared its unilateral cease-fire.

Nor are they ready to forewear the use of the area south of the Litani River for attacks against Israel.

Farouk Kaddoumi, the head of the Palestine Liberation Organization's political department, told a Beirut magazine this weekend that it might be possible to renegotiate the so-called Cairo accords of 1970 governing the Palestinian presence in Lebanon - but only when the Israeli withdrawal is completed.

Further potential trouble is represented by the continued Palestiman presence in the approximately 5200-square-mile area located between the Litani and the Zahrani River to the north.

All U.N. lines of communications inside Lebanon now must go through that territory.

The most eloquent proof of the dangers involved was provided by Waldehim's travel schedule. Instead of driving south from Beirut down the coastal road to visit U.N. units south of the Litani, he chosse to fly to Israel and approach them from the more secure Israeli side.

Yet another gray area, which Waldheim in his news conference brushed aside as hypothetical, centers on what the U.N. peacekeeping force should do about the Israeli-Lebanese border.

For more than 18 months, Israel has maintained a so-called "good-fence" at the frontier through which it has supplied its Christian Lebanese allies with tanks, artillery, ammunition, food and financing.

Some Lebanese argue that helping restore Lebanese authority - as the Security Council enjoined the mission - could mean closing the frontier. It is doubtful that Israel would comply.

Finally, the Lebanese government is upset at Israel's recent announcement that its territory is now subject to U.N. Security Council Resolution 242.

That resolution, voted at the end of the six-day Arab-Israeli war in 1967 in which Lebanon took on part, called for the return of Arab territory occupied by Israel in return for recognition of Israel's right to exist.

The recent Israeli stand, the Lebanese government fears, suggest that Israel does not intend to withdraw completey from Lebanon and instead seeks to make total evacuation dependent on the still far-off possibility of an overall Arab-Israeli peace settlement.