Prospects for real democracy in this nation of 35 million look no brighter now, as Iran moves into its third month as an Islamic republic, than they did under the shah.

The resignation today of Foreign Minister Karim Sanjabi and demonstrations in support of liberal Ayatollah Mahmoud Taleghani indicate that there is also no end in sight to the potitical instability here.

On the surface, Tehran, two months after the armed overthrow of the monarchy, looks normal.

But beneath that veneer, serious problems-economic and political-threaten the stability of the new Iran and make it unlikly the county will turn out any more democratic than most other Third World States.

Among the gravest problems for the new government, diplomatic observers say, is the ability of restive tribes and regional groups demanding autonomy to harass the beleaguered central authorities.

The government's regional problems highlight what is undoubtedly its top priority: establishment of a force loyal to the central authorities and capable of maintaining public order.

The government is trying to do this by rebuilding the armed forces as they were under the shah. But Iran's powerful guerrilla groups are resisting this, trying instead to create a people's army" run by soldier committees and elected officers.

Such a system would give the guerrillas the opportunity to take control of the armed forces gradually. So far, the two main groups, the Islamic Mujaheddin-e-Khalq and the Marxist Fedaye, have recruited enough memebers within the military to stymie the government's efforts.

The two guerrilla groups are competing for control of the army's lower ranks. The larger of the two, the Mujaheddin, basically follows the line of Ayatollah Ruhollah Khomeini. It is an independent group, however, and has a more socialist revolutionary vision of Islamic society than does Khomeini or his prime minister, Mehdi Bazargan. The Fedaye, on the other hand, seeks a proletarian revolution leading to a communist state.

The desire of both groups for a new economic structure is frustrating the government's efforts to put the country back to work. The issue is who should run Iran's industries and economic institutions: tradtional management or new workers' committees?

The failure to agree on this question has fueled unemployment-now estimated at about 50 percent of the work force. Jobless Iranian workers have staged increasingly angry demonstrations in recent weeks and are becoming an ever more serious problem for the government.

Given the present circumstances some observers believe the wave of trials and summary executions of officials and supporters of the deposed shah is largely intended to distract public attention from the new regime's inability to solve its problems.

The problem with that is it is alienating moderates and liberals in the middle class and government, which seems powerless to intervene. Prime Minister Bazargan, once Iran's leading human right advocate, is forced to preside over a system that denies its adversaries the very rigts he fought for against the shah.

Khomeini's revolutionary committees, working separately from the government, have been carrying out the trials and ecxecutions and interfering in government affairs at every turn.

Although many educated Iranians privately express horror at the way the trials and executions are carried out, they are largely afraid to speak out, afraid of being branded "counter-revolutionaries" and perhaps becoming victims themselves.

For most Iranians, though, the question is hwether there is more freedom now than under the shah. On balance, the answer is yes. There is freedom of the press, of association, of political parties.

But there are limits to the new freedom. Radio and television is still censored, the press is not free to criticize Khomeini, new decrees impose Islamic rules on the populace and, most importantly, there is effectively no rule of law.

Liberal Iranians place their hopes for turning Iran into a more democratic contry in the election June 1 for a constituent assemble and the vote later for a new parliament and the country's first president.

But there seems little to ensure that in these votes there will be any more freedom of choice than in the recent balloting that brought the Islamic republic into existence, offering the deposed monarchy as the only other alternative.

And it appears even less likely that Khomeini and his entourage, who enjoy the support of a majority of Iranians, will give up any of the supra-governmental powers they now hold. CAPTION: Picture, Students in Tehran demonstrate in support of liberal Ayatollah Taleghani. AP