In most shows, there is some sort of ongoing mystery that will never really be elucidated. In my opinion, there is something to understand other than just comic-effect. Let's take a quick look at different mysteries and see how they impact a sitcom.
The Simpsons never say in which US State they are. This could be unimportant, but they insure that you keep wondering with different allusions and try to maintain the mystery alive.
In The Big Bang Theory, there used to be a mystery about how the elevator stopped working but it was resolved recently. There is however the fact that Howard's mother is always heard but never seen.