From what I've been able to find online, the employer does have a legal obligation to protect the nurse from sexual harassment by patients.
"According to the EEOC
, an employer may be responsible for harassment by nonemployees in the workplace if the employer fails to take corrective action, within its control, once it knows or has reason to know of the harassing conduct. ... When faced with the novel issue of sexual harassment by nonemployees, several courts have specifically identified the EEOC guidelines as their authority for holding an employer liable."
Another article says that "federal and state laws protect nurses
from sexual harassment by patients, and the institutions' written guidelines must reflect those laws." This article also says that in extreme cases, institutions can "fire" a harassing patient and send him to another institution.
I don't see how being asked to turn on a VCR or posting a sign could be construed as harassment. But it appears the institution does have a legal obligation to tell the patient to knock off the lewd behavior toward nurses; otherwise, it's allowing a hostile work environment to persist.