Problem loans, many of them to Mexico and Argentina, contributed to a 30 percent decline in Chase Manhattan Corp.'s fourth quarter earnings and a 25 percent decline for all 1982, the giant bank holding company reported yesterday.

Chase, which owns the nation's third largest bank, said fourth quarter earnings were $108 million before securities transactions compared with a record $154 million in the final three months of 1981. The 1981 quarter included an $18.5 million, one-time gain. Even after that gain is excluded, however, profits at Chase declined 20 percent.

Last year was the giant bank company's most troubled since 1976. For the year, Chase's profits before securities transactions were $332 million, down from $444 million in 1981. The bank reported $117 million in losses after the failure of its client Drysdale Government Securities Inc. last May and bought more than $200 million in questionable loans from Penn Square National Bank of Oklahoma City, which failed July 5. Most of the losses on Drysdale and Penn Square were accounted for in the second and third quarters.

The fourth quarter earnings slide related to the failure to receive interest on about $300 million in loans made to Mexico and Argentina, as well as a $15 million increase in its regular provision for problem loans to $78 million, from $63 million in the last three months of 1981.

The bank said that its problem loans--those paying no interest or reduced interest--cost it $75 million in 1982 earnings, compared with $47 million in 1981.

Chase said it did not credit its books with about $16 million in interest ($8 million after taxes) that was due on about $300 million in loans to private Mexican borrowers and to the Argentinian public sector. But the bank took the unusual step of not adding these loans to its list of nonperforming assets.

Normally, a bank "accrues" interest on good loans daily, even though the borrower may pay only quarterly or yearly. If a loan is put on a cash basis, so that the bank only records the interest when it is actually received, the loan is usually classified as "nonperforming." Chase added $200 million in loans to its nonperforming list in the fourth quarter. There are now about $1.4 billion in problem loans on Chase's books.