Width is a major issue, but you're already wide with most truck campers, regardless of the truck.
Ruts as mentioned, but I've found them not to be a big issue. I've been in one or two precarious situations due to ruts but came out fine.
You can't air down too much, because the duals might touch, or you might have 19.5s (same goes for a lot of SRW TC haulers).
Rocks can get stuck between duals, but I've only had that happen once where it was wedged enough to stay for any length of time and it still didn't do any major damage.
Unloaded, you have half the weight per inch of contact (not exactly 50% due to the SRWs usually running slightly wider tires). That can cause traction problems. Loaded with a heavy TC, it's less of an issue.
Dually trucks usually ship with slightly shorter tires than their SRW counterparts. That can make it more difficult to climb tall obstacles.
On the flip side, I've found the stability of the dually makes it easier to take a top-heavy load further off the beaten path. With a heavy TC, I have a ton of weight on each of my tires and rarely run into traction issues. If I can fit and climb over obstacles without bottoming out, I generally make it. Due to the long wheel base (a long bed crew cab truck problem, not dually specific) I've used my steps as rockers a time or two and they're kind of beat up.