My two cents on this (hi, btw): I've never really been bothered by episodic stories that remain in relatively static time periods, because I've always figured that only the exceptional events are depicted. There are probably long stretches of time where it's just Marten, Pintsize, and Faye sitting on a couch, watching TV and screwing around on their phones. We don't get to see that because it's uninteresting, without conflict there is no story, etc.
Part of what I really like about QC is the setting. It may be in the past to us chronologically, but Jeph had the awesome idea of making their technology advanced while keeping their social culture relatively the same. The get to have all the latest devices because, in the setting of QC, iPhones probably came out in, like, the early 80s and nowadays you can get them in the checkout aisle at Target for $3. It also presents interesting storytelling opportunities, like the fact that they probably have more advanced medicine, but receiving treatment is still hampered by their lack of healthcare reform (hence Dora letting Faye stay on the books so CoD's insurance will cover her).