I feel I should chime in and give my experiences from the 1.3k miles I have on my new Limited.
When I test-drove this Ram, I noticed the vibrations between about 56 to 65 mph immediately. It is only a slight vibration/nothing serious and so far my wife and kids have not commented on it, but was enough for me to notice even when I wasn't looking for it. Unfortunately for me, I travel in that speed range every day when I go to work...so I wasn't happy. The only time it wouldn't vibrate was when I was under load while towing my travel trailer. The dealer said they'd take care of re-balancing the tires for me, but I didn't want to hassle with it (yet) since I knew I was getting new tires.
About 2 weeks ago, I had the new larger & e-rated tires installed by a local auto shop (not the dealer). I am happy to report that the vibrations are now completely gone! Well, at least 80mph and below. I have yet to get it above 80 mph...but that won't be happening until I travel to another state with a higher speed limit.
I know some in this thread seem to have worse vibration issues what I was experiencing...but if you are able, changing tires might be a solution for some.
This made me especially happy since we had similar issues with the 3rd Gen Tacoma's. The vibrations happened at slower speeds (in the 40's), but wheel/tire balancing and/or changes did nothing. It wasn't until 2 different people changed out their entire drive shaft that we started to see positive results. I think it eventually became a TSB, but I was already looking to sell it and didn't want to go through the hassle with the dealer.