KANSAS CITY, Mo. (AP) _ The Marine Corps Finance Center has made millions of dollars in pay errors involving military personnel and retirees in recent years, according to a published report.

Marine audits revealed the Corps made overpayments and underpayments to active-duty Marines estimated at $100 million in 1983 and almost $126 million in 1982, the Kansas City Star said in a copyright story Sunday.

Pay errors during the first half of 1984 - the most recent period when such statistics were available - totaled about $30 million, the newspaper said.

Marine officials acknowledged mistakes had occurred, but said the errors represented a small portion of the estimated $3.9 billion in payroll and related payments disbursed in 1984. Those receiving payment included 195,000 active-duty Marines, 102,000 reservists and 91,000 retirees and their survivors in 1984.

''What is an acceptable error rate?'' said Col. Lynn Mertes, commanding officer of the Kansas City-based finance center. ''If you look at a $3 billion appropriation and you're looking at an error rate of 1 percent, what does that equate to? More money than we'll make in our lives.''

Problems in the Marine pay system had been outlined in nearly 90 reports issued from 1978 to 1984 by the General Accounting Office, the Naval Audit Service and internal Navy and Marine Corps auditors, the newspaper said.

Marine officials do not keep track of how much of the mistaken pay is recovered, but they said the center was trying to collect more than $9 million in overpayments from former Marines as of April 30.

Officials at Marine Corps headquarters in Washington rebutted criticism of the finance center's operations.

''The information we have on the Marine Corps Finance Center would suggest they're doing an exceedingly good job in what they do,'' said Col. George K. Robinson Jr., head of disbursing for the Marine Corps.

Raymond Butts, national executive director of the Marine Corps League, an independent service organization, said the finance center seemed to be a ''very well-oiled machine.''

But Randall Moudy, a former private first class from Jacksonville, N.C., said Marines in his unit frequently encountered pay problems.

''There were generally 10 or 20 people or more (whose) pay was screwed up,'' said Moudy, who served as a helicopter mechanic before leaving the service in January. ''Whenever you move from one duty station to another, you can count on your pay not being right for half a year. People expect it.''

The newspaper said the Corps was trying to improve record-keeping in the field by installing computer terminals that would give outlying offices access to central computers in Kansas City.