President Reagan sets off for the Far East this week amid continuing frictions in Japanese-American relations. He is not expected to highlight these during a visit billed largely as a reaffirmation of the strong and cooperative ties between Japan and the United States. But the problems will form the backdrop for bilateral talks:
* The US this year is running a trade deficit with Japan of more than $22 billion. Washington policymakers see Japan, despite its recent agreement to curb auto exports to the US for a fourth year, as still reluctant to open up its markets to American goods, especially food.
* Washington is also impatient with the pace of Japan's military buildup. Japan agreed in May 1981 to boost its defense spending in order to have the capacity to protect itself and sea lanes up to 1,000 miles from its shores. But since then it has reduced the rate of increase in defense spending because of domestic financial pressures.
Administration officials say that Mr. Reagan will not make a frontal issue of trade or other problems. Instead he will try - through a high-toned visit - to help Japanese Prime Minister Yasuhiro Nakasone, who is facing his own brand of domestic political problems. The hope here is that the Japanese leader will do the same for Reagan during the 1984 election year.
''We'll scratch his back this year and he'll scratch ours next,'' a senior White House official comments.
The Reagan administration is sensitive to the fact that Mr. Nakasone is fighting a political battle against former Prime Minister Kakuei Tanaka, who refuses to give up his Diet seat following a conviction on bribery charges. Reagan's visit could enhance Nakasone's stature, benefiting him politically if he calls elections later this year. Any confrontational pressure from the US, on the other hand, could harm him.
For his part, Reagan is under mounting pressure from US farmers and manufacturers to pry open Japanese markets to more of their commodities. He also faces a feisty Congress increasingly determined to adopt protectionist measures, which would undermine the administration's efforts to expand global trade. If Japan further liberalizes its trade policies next year, Reagan will have added political capital in the American farm and industrial belts.
Japanese exports to the US are growing at a rate of 16 percent a year, while American exports to Japan have expanded at a rate of only 9 percent, creating a wide trade imbalance. American officials are especially concerned about Japan's high subsidization of its farmers and the consequent reduced Japanese market for US farm products. They also point to Japanese inspection and certification standards for foreign imports that effectively keep out some US manufactures.
But the larger cause of the trade problem is seen to be the overvalued American dollar in relation to the yen. The dollar has appreciated about 20 percent against the yen in the past several years. American products thus cost more relative to Japanese goods. David Packard, US chairman of the US-Japan Advisory Commission, estimates that the imbalance in American-Japanese trade is costing the US some 2 million jobs. ''If the yen-dollar relationship could be corrected, it could be a very important factor in improving the job situation here in the United States,'' he said last month.
Still, some economists say they think the trade issue is being exaggerated. ''It's a vastly overstated problem,'' says William R. Cline of the Institute for International Economics. ''We export as much in manufactures to Japan as we do to Germany, so the public perception that Japan is very protective is broadly wrong. The Japanese market is not all that closed.''
Even if there were a total liberalization of the Japanese market, says Mr. Cline, the net effect would be modest. Japanese imports of US goods might increase by $3 billion or $4 billion a year out of a total two-way trade running well over $50 billion.
Defense issues are also on the agenda. Reagan will stress the US commitment to stability and security in East Asia. He will seek to reassure the Japanese that the US will not reach an accord with the Soviet Union on medium-range nuclear missiles in Europe that increases the threat of the Soviet SS-20s aimed at Asia.
At the same time US officials are concerned about Japan's own defense effort. Japan now has the eighth-largest defense budget in the world and it has agreed to take on larger defense responsibilities. But Washington is unhappy with the speed of the military buildup.
''The problem is capability,'' says a Defense Department official. ''Japan can't carry out its roles at present. It has 13 divisions and that's enough. But it has only one week's supply of ammunition. It also doesn't have the torpedoes and missiles to protect sea lines up to 1,000 miles. So it does need to do more. That probably means more money.''
These bilateral questions are expected to be dealt with only in general terms. Administration officials stress that the focus of the Reagan visit will be on the strong US-Japanese partnership in the international as well as bilateral arena.