Like many Black and rural Americans, Denese Rankin, a 55-year-old retired bookkeeper and receptionist in Castleberry, Ala., did not want the Covid-19 vaccine.

Ms. Rankin worried about side effects — she had seen stories on social media about people developing Bell’s palsy, for example, after they were vaccinated. She thought the vaccines had come about too quickly to be safe. And she worried that the vaccinations might turn out to be another example in the government’s long history of medical experimentation on Black people.

In Florida, less than one-quarter of delivered coronavirus vaccines have been used, even as older people sat in lawn chairs all night waiting for their shots. In Puerto Rico, last week’s vaccine shipments did not arrive until the workers who would have administered them had left for the Christmas holiday. In California, doctors are worried about whether there will be enough hospital staff members to both administer vaccines and tend to the swelling number of Covid-19 patients.