IN October the Port of Seattle made a record with 107,709 20-foot equivalent units (TEUs) of containers crossing the docks at port-owned facilities. The previous record was October 1990 when 103,008 containers passed through the region's leading gateway to destinations across North America and throughout the Pacific Rim. ''October's success comes on the heels of a great summer when our volumes for August and September were records for each of these months,'' said Don Fleming, managing director of the port's marine division. ''This is the fifth time in port history that container volumes handled in a single month have surpassed 100,000 TEUs.'' Records tumbled in August and September with volumes of 101,995 and 94,741 TEUs, respectively. ''The October record is the result of growth and changes by our steamship lines and excellent work by everyone involved in the trade - longshoremen, warehousemen, truckers, rail workers, and businesses which choose to import and export through this gateway,'' said Bob Koplowitz, director of marine marketing and business development for the port. ''We're pleased to be a catalyst in the 'trade chain', by creating partnerships and providing the infrastructure that results in commerce,'' he added.