The initial screening process, now on its fifth day, has been stymied by a host of challenges and distractions, including repeatedly denied requests from the defence and a noisy protest outside the courthouse.
Both sides hope to deliver opening statements before the end of the month.
If convicted at a trial expected to last into March, the 67-year-old could face life in prison.
The former studio boss behind such Oscar winners as Pulp Fiction and Shakespeare in Love has said any sexual activity was consensual.
About 120 prospective jurors are being summoned to court each day. Last Tuesday, they were introduced as a group to Weinstein and were read a list of names that could come up at trial, including actresses Salma Hayek, Charlize Theron and Rosie Perez.
Those charges accuse him of raping one woman and sexually assaulting another woman there on back-to-back nights in 2013, days before he walked the Oscars with his then-wife, fashion designer Georgina Chapman, who was pregnant at the time.
Weinstein has not entered a plea in the Los Angeles case, which will be tried later.