Rent Control, birth control
I can't help thinking two things: immortal people must have incredibly cheap rent, what with New York City rent control, and, considering how many of Amsterdam's kids I've seen in just the first two episodes, what are the odds that his descendants are a good portion of the city's population? Oh, of course that brings up one more: does he keep track of his descendants so that he can avoid sleeping with any of them, or is it like "kissing cousins", and beyond a certain degree doesn't matter?
(Yes, I like the show ans am sorry it's gone, but I'm a history, SF, and crime buff.)