Washington — Three broad issues concern Mexico and the United States as Mexican President Miguel de la Madrid Hurtado pays his first official visit to Washington:
* Despite its austerity program, Mexico continues to wrestle with a mammoth $ 90 billion debt and will require special treatment from the United States to handle repayments. It also seeks relief from US trade restrictions.
* The two nations have different views of how to deal with communist subversion in Central America. Mexico, one of the four so-called Contadora nations working for a negotiated settlement, has strongly criticized the use of American military force in the region.
* The United States is increasingly concerned about the unrelenting influx of illegal immigrants across the 2,000-mile border. Mexico is sympathetic to the problem but says the solution lies in strong economic cooperation that will make possible the growth of jobs in Mexico and alleviate the pressure to migrate. It also voices concern about the labor rights of Mexican workers in the United States.
Despite these concerns, relations between the two nations are fundamentally good. And as President de la Madrid goes through a round of high-level talks and appearances, including an address to Congress on Wednesday, he is not expected to rock the boat of US economic help by engaging in strong public criticism of administration policy.
President Reagan and the Mexican leader began their talks Tuesday by focusing attention on Central America. In a 40-minute one-on-one meeting, the two laid out their views and, according to a senior administration official, agreed that the ''search for peace'' in the region was the ''primary objective'' of both countries.
The two have ''faith in each other'' and a ''warm personal understanding,'' the official said. This was their third meeting. The first took place near the US-Mexican border in 1982 and the second last year in the Mexican city of La Paz.
While at this writing it was not known what the two leaders said in their private conversation, their differing approaches to the Central America dilemma surfaced during the welcoming ceremony. Mr. Reagan endorsed the efforts of the Contadora group but stressed the communist threat.
''Responsible governments of this hemisphere cannot afford to close their eyes to what is happening or be lulled by unrealistic optimism,'' he declared. ''For the United States, the conflagration in Central America is too close to ignore. Like a fire in one's neighborhood, this threat should be of concern to every nation in the hemisphere.''
President de la Madrid, for his part, chose to stress the dangers of foreign intervention and of a general war in the region. ''Every country on the continent must do its utmost to restore peace and avoid war by respecting and upholding the sovereign right of its people to decide their own destiny and by rejecting interventionist solutions of any kind,'' he said.
It is economic matters that will dominate the bilateral talks, however. Mexico believes that the only way to overcome its severe debt problem is to boost its exports abroad. But exports to the US are subject to so-called countervailing duties when US industries claim that they they are being subject to unfair competition from Mexican producers who receive government subsidies.
Administration officials say that the two nations are close to reaching a subsidies agreement on such nonagriculture items as steel, cement, and toy balloons. Under it, US companies would have to prove that Mexico is subsidizing exports and that they are suffering harm as a result. This is how the subsidy issue is handled under the General Agreement on Tariffs and Trade, of which Mexico is not a member.
A subsidies agreement, as well as US assurances that Mexico will continue to receive special tariff treatment for certain exports, are extremely important to President de la Madrid. Mexico has come around to realize that it cannot continue heavy borrowing in order to subsidize domestic consumption and that it must generate more internal investment through exports rather than loans.
Paying off its whopping loan also poses a continuing problem. US banks granted Mexico concessions on its 1984 loan repayment obligation, because Mexico is vigorously trying to put its economy in order. But the recent rise in the prime rate has already wiped out the value of those concessions.
Illegal immigration poses perhaps the most acute long-term problem for the US in its relations with Mexico.
The official Mexican position is not to argue openly about an issue pending in the US Congress. But it is expected to be raised in private discussions. In early June, the House is due to consider again the controversial Simpson-Mazzoli bill, which seeks to discourage illegal immigration by penalizing employers to hire illegal aliens.
President de la Madrid has expressed concern about solutions to the problem that ''infringe on human rights.''