The first overnight of the Washington Square Park female turned out to be a premature stay on the nest as she skipped at least the next two nights. While this is the first time I've seen a hawk spend a night on a nest and not return, I don't think it is a cause for concern. Either Wednesday's Peregrine battle or large protest in the park could have caused the female to feel a need to occupy/protect the nest for the night.
This evening, both hawks were very active and were being a couple by sharing perches and food. It looked like things were back to normal for late winter. I suspect brooding will start within a week.
Update 3/11/17: The first egg was seen on the nest Saturday afternoon around 1 p.m.