It looks like Epstein had four or five years of college at Cooper Union (1969-1971) and at NYU’s mathematics institute (1971-1974), possibly taking off some time in between. Dalton may have taken him on with the proviso that he finish up his degree if he wanted to keep his job. That’s rare for high schools and bachelor’s degrees, but I believe it’s common for colleges to hire post-grads who haven’t yet finished their degrees. And Dalton, remember, was a progressive school that may have wanted to show that bureaucratic details didn’t matter.
One thing to note is that prep schools in general were REALLY hurting at this time. The baby boom had trailed off, prep schools themselves were sneered at in some circles, and the economy was suffering. My own prep school went from a height of 1,200 students in 1964 to a low of under 250 in the mid-70s, and that was despite turning co-ed. Teachers, therefore were not as in demand, and even at the top levels, the pay generally stinks, and it isn’t a 40 hour job, when you are asked to coach lacrosse or be a dorm master. Even New York was hurting in those days (read “Art of the Deal”), but I would think that area would be most resistant to a downturn.
Every state has different requirements for teachers. In this time frame, it may not have been uncommon to hire teachers who had a few years of college if they were qualified in the subject matter. Even now, in many states, substitute teachers do not have to have credentials.