Saddam Hussein, the debonair 43-year-old strongman of Iraq, inspires decidedly mixed reviews.

Critics, mindful of foes executed by the score, call him the "Butcher of Baghdad." Supporters say that more than any other Arab leader he eschews visionary goals to focus on getting from where he's at to where he wants to be. "Dignity" and "pride," they point out, are not his characteristic words so much as "starting point," "outcome," "line of march," "strategy" and "calculation." They call him, as he does himself, "an engineer of revolution."

But even these qualities have not served to carry him easily across the turbulent currents of inter-Arab politics. His recent effort to use the occasion of Egypt's treaty with Israel as a way of putting Iraq atop the Arab world has not paid off.

Many considerations favored Saddam's bid for power. Iraq is situated at the fulcrum of the Mideast -- the place where the lands of the Fertile Crescent merge with the oil countries of the Persian Gulf. As a major oil exporter (second, with 3.5 million barrels daily, only to Saudi Arabia), it has the scratch to help out such needy cases as King Hussein of Jordan, Yassar Arafat of the Palestine Liberation Organization and Hafez Assad of Syria.

A reputation as a revolutionary gave Saddam an opening to the "progressive" regimes in Syria, Libya, South Yemen and Algeria. A strong army, and commandos of guns for hire, put him in position to threaten and protect Saudi Arabia, Kuwait and the weaker sheikdoms of the Persian Gulf. The more so as for years he had played off the Russians (from whom he bought arms) against the West (with which he did business).

Striking success initially crowned the Iraqi bid for Arab leadership. At summit meetings in Baghdad in 1978 in last year, most of the Arab countries joined Iraq in condemning Sadat's "separate peace" with Israel. A program for unity between Syria and Iraq was initiated. Common oil policies were worked out with Saudi Arabia. On March 8 of this year, Saddam issued an eight-point Arab charter, designed to hold Russia and the United States out of the Persian Gulf, while casting Iraq in the lead role as the protecting power of the area.

But the Iraqi regime is a secular affair run almost exclusively by Moslems of Sunni sect. It was thus vulnerable to Islamic fundamentalism preached across the border by Ayatollah Khomeini -- especially since Khomeini is a Shia with a potent appeal to the largely Shiite population of southern Iraq.

Much as he struck out the United States when internal troubles developed, the ayatollah also picked on Iraq. Several times Radio Tehran has announced Iraqi attacks on Iran. Though exaggerated if not altogether false, the reports of attacks have caused Iraq to take precautions, including some boarder raids probably aimed at the sabotage of Iranian oil installations. In retaliation, Iranian sympathiziers here have tried to assassinate a number of Iraqi leaders, including Saddam Hussein himself.

The Baghdad-Damascus connection is even more tense. In moving from strongman to president last July, Saddam Hussein executed 20 former associates on the grounds that they had plotted against Iraq with the Syrians. Iraqis have subsequently backed the internal opposition to the present Syrian leadership, and Iraq seems to have had at least some hand in the series of assassinations and protest strikes that have shaken the regime.

The syrians have responded, first, by tightening their links to Moscow and, next, by the old technique of one-upsmanship on the hot issue of Palestine. In Tropoli last week, the Syrian leader met with the other radical leaders from Libya, Algeria, South Yemen and the PLO to affirm the strongest possible stance against the Egyptian-Israeli treaty. In the process, they took a shot at Saddam Hussein and his eight-point arab charter on the grounds that it meant collaboration with the reactionary regimes of the Persian Gulf.

The result is a three-way split in the Arab world. Anwar Sadat's Egypt -- moving toward settlement with Israel under American auspices -- represents one current. Saddam Hussein -- pushing for a non-aligned grouping of arab nations -- represents a second current. Then there is the radical current, led by Syria with a boost from the Soviet Union.

Each approach cancels out the others. None of the roads now open in the Arab world leads anywhere. The prospect for any kind of settlement now seems extremely remote, and the real issue is whether a catastrophic upheaval can be avoided.