I looked into doing this and ultimately decided it was too much of a hassle, so we went with an agency, but this was back in the day before I was Mustachian and gladly paid people to do things I didn't want to do.
The only thing I can think of that's missing is unemployment insurance--not sure if this varies by state or not, but if we'd done it independently, we would have been required to pay for unemployment insurance for the nanny.