PARIS: [sleep talking in background] Woodward . . . Bernstein . . . Harry Thomason.
LORELAI: Is that Paris?
RORY: Yeah, she talks in her sleep . . . long in-depth arguments.
Paris references Bob Woodward and Carl Bernstein, previously mentioned, the journalists who broke the story of Richard Nixon and Watergate.
Harry Thomason (born 1940) [pictured], film and television director and producer, best known for the sitcom Designing Women (1986-1993). Thomason and his wife, Linda Bloodworth-Thomason, are close friends with former President Bill Clinton and his wife Hillary, the former Secretary of State, playing a major role in President Clinton’s election campaign. He produced a glowing biographical film called The Man From Hope, the centrepiece of the 1992 Democratic National Convention. Thomason served as co-chairman of the 1992 Presidential Inauguration Committee.
It is not completely clear whether Paris is arguing with Woodward, Bernstein, and Thomason in her dreams, or if she is quoting them in support of her dream arguments. I think the second?