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Weinstein (67) has pleaded not guilty to charges of assaulting two women, and faces life in prison if convicted on the most serious charge, predatory sexual assault.
Since 2017, more than 80 women, including many famous actresses, have accused him of sexual misconduct dating back decades.
Weinstein has denied the allegations, saying any sexual encounters he had were consensual.
The allegations helped fuel the #MeToo movement, in which women have gone public with misconduct allegations against powerful men in business, entertainment and politics.
"This trial is not a referendum on the #MeToo movement," James Burke told the potential jurors on Thursday. "You must decide this case on the evidence."
Earlier in the morning, the judge ordered one man in the jury pool to appear in court on March 10 after he tweeted about using jury service to promote a book. Burke told the man that he could face a fine or up to 30 days in jail.
The jury pool included supermodel Gigi Hadid, though she was excused from service shortly after reporting to court.
The jurors were chosen from a pool of about 140 people who passed a pre-screening process. Prosecutors, Weinstein's lawyers and Burke are striving to select 12 jurors and six alternates before opening statements, which are expected to begin on January 22
Weinstein's trial began on January 6 and is expected to last up to two months.
Legal experts have said selecting impartial jurors in a case that has attracted a great deal of publicity could be difficult.
Weinstein, once one of Hollywood's most powerful producers, made his mark with critically acclaimed films such as The English Patient and Shakespeare in Love.
On January 6, as the New York trial began, Los Angeles District Attorney Jackie Lacey announced new sexual assault charges against Weinstein.
On Wednesday, Weinstein filed a last-minute motion with a New York appellate court to have his trial delayed and moved out of Manhattan, arguing that the "carnival-like atmosphere" surrounding the case made it impossible for him to get a fair trial.
The court has not ruled.