What time period is Gotham set in?
Gotham showrunner Bruno Heller explained this to Entertainment Weekly some time ago:
Gotham is not set in any particular time period: Okay, this has been out there a bit, but Heller had a nice quote elaborating on the show’s timeless quality: “It’s a mash-up, to use the modern phrase,” he said. “If today Batman exists, then this world is the past. But it’s everybody’s past, an 18-year-old’s past and a 54-year-old’s past. So in your memory, the past is all mashed up together. So in this Gotham, it’s a kind of timeless world. It’s yesterday, it’s today, and it’s tomorrow all at the same time, because that’s the world that dreams live in.”
That's interesting. I hadn't seen the quote before, but noticed the "mash-up" in last week's episode. The entire office was using typewriters, and all the cars were the 80s box-style. But then Gordon pulls out a cell phone.