He was a law clerk for Judge Leonard I. Garth on the United States Court of Appeals for the Third Circuit from 1975 to 1976.

He was an assistant United States attorney for the District of New Jersey from 1976 to 1982.

He was in private practice in Wayne, New Jersey from 1982 to 1985, and was then again an assistant United States attorney, this time in the Southern District of California, from 1985 to 1988.

From 1986 to 1995, Moskowitz was a United States magistrate judge of the Southern District of California.

On June 30, 1995, Moskowitz was nominated by President Bill Clinton to a new seat on the United States District Court for the Southern District of California created by 104 Stat.