The Supreme Court agreed Monday to decide how much influence the American Bar Association should have in the judicial selection process, an issue that could affect the way the president picks federal court nominees.

The justices will hear arguments this term in appeals by two Washington, D.C., interest groups opposed to the ABA's heavy influence in the nominating process.The interest groups, the liberal Public Citizen and the conservative Washington Legal Foundation, are appealing a federal district court ruling upholding the Justice Department's relationship with the ABA Standing Committee on Federal Judiciary.

During recent years, the committee has come under fire from both the left and the right for being alternately a rubber stamp for the Reagan administration or too partisan and liberal in its political leanings.

The standing committee has traditionally investigated prospective nominees for federal district courts, appeals courts and the Supreme Court and rates them according to their legal qualifications.

The ratings are not binding but play a major role in the Justice Department's decision to recommend candidates and the president's ultimate decisions on whom to nominate.

The judicial nominating case arose in 1986 when the Washington Legal Foundation filed suit against the Justice Department alleging that its reliance on the ABA committee was improper because the committee does not comply with regulations of the Federal Advisory Committee Act. Among other things, the act requires committees that advise the government to hold public proceedings.

In a decision issued Aug. 4, 1988, District Judge Joyce Hens Green concluded that the ABA committee is an advisory committee that would normally fall under the provisions of the FACA. But she said to apply the FACA would be unconstitutional because it would violate the separation of powers between the branches of government.

In urging the high court to take up the matter, lawyers for Public Citizen said the lower court ruling "insulates an advisory body of paramount importance to the public from an entire regulatory scheme. Of even graver concern, the district court's ruling suggests, for the first time, that any activities touching in any manner on the president's power are beyond the ability of Congress to regulate in any aspect."

The justices also:

- Stepped into the tangled issue of what constitutes excessive damages in a case that levied $6 million in damages against a trash hauling firm for its role in a predatory pricing scheme.

-Refused to allow a lawsuit by the families of two federal agents killed during a 1986 gunbattle in Miami that also left the two suspects dead.

-Rejected a plea to revive portions of the Tennessee textbook case involving claims by fundamentalist Christians that public school textbooks violate their religious beliefs.