Great idea for the double wall tent, Glenn! (I haven't used one in a while). For a single wall tent, wipe down the inside walls if necessary; wipe off the outside just before taking it down (unless it's raining hard at the time) and then give it a good shake just before stuffing. Of course, you'll have everything else packed up and inside your pack before you take the tent down! And of course you have some kind of towel (I prefer "Handi-Wipes" because they're lighter and dry faster) to do this with!

The wet tent issue is one reason I use one of the outside side pockets of my pack for my tent. A second reason is that I want to be able to get at my tent and set it up without opening my pack should it be raining. A third reason is to be able to stop and dry it out should a "sun break" occur during the day.