A friend asked me what this plant is. I said Night Blooming Cereus. Now I'm not so sure, mainly because of the "tassles" on the ends of the leaves. Is it a Night Blooming Cereus or something else?

I think it is and they just do that sometimes.

There are many plants with that common name. It looks like an Epiphyllum to me (no kind of Cereus) and it looks desperate for more light (skinny stems are stretching). Ideally the whole plant should "see" the sun for hours a day year round indoors, with no curtain or blinds in the way.

That makes sense, it's being kept in a bathtub at the moment. Thanks for your help.