Do missions change if you wait?
Solution 1:
First, unintercepted sites vanish after a time. So that's one big change. The other change is day/night. But other than that, no, each landing starts "fresh", a terror site will be as fresh after 20 hours of waiting for your team as when the aliens landed.
Note as you load your game and intercept the same site again, the map might have changed, but that's not time dependent really, it's just the random choice of a map.