Mine is a 2007, just had it in the body shop today and had it looked over again, the guy found that it was hit hard on that side and the A-Pillar flexs when we open and close the door, so something is screwed up in there. I gotta take it and leave it next week for a few days and the shop is gonna tear it down and figure out what wasn't put together correctly when the previous owner fixed it. Hopefully they can fix it cause so far this is looking to be a more serious problem than a sagging door.

 

The seals around doors and atop the doors front to back go flat after time.
But I came up with a cheep fix.
The seals are hallow so first remove the seals from the truck 2 or 4 lay them out strait on the floor you will need to put a weight on one end and stretch out, run a fish tape all the way though and out the end.
O you will need to go to hardware store and get 1 package of 3/8" foam snake per door and 1 package of 1/2" for the top seals. Tops need not be removed.connect snake to fish tape and you will need a little lubrication pam cooking spray or something similar but nothing with petroleum base.
tie wire can be used if you do not have fish tape just loop the end back on itself as not to poke a hole.
GOOD LUCK

 

I wouldn't spend much time and money on body work to fix your leaky door problem. Just about every newer style Dodge does the same thing. As someone said earlier, it's mostly in a cross wind. The reason? Look at the top edge of the doors, how they stick up over a quarter inch above the cab. The wind hits that edge and flexes the door enough to leak air. And as someone else said earlier, if you tweak the top of the door in "just a little" it will solve the problem.
I've had two newer Dodges that have done the same thing, and ridden in others that also do it. Probably has nothing to do with it being previously wrecked. As a Dodge fan, I have to admit, it is just a bad design!

 

My '04 leaks air around the driver's window occasionally. I can roll it down an inch or two and then back up, and it seems to fix it.