If you are pulling a 5th wheel be aware some tunnels are not as tall on the sides as they are in the middle.  Also like another post mentioned,  many of the access roads leading to and from the parkway would be a nightmare for a 5th wheel.  Once you are on the parkway generally speaking there is only one place I can think of you should use caution.  Mile marker 75 you will be at the highest point on the BRP in Virginia,  15 miles later you are at the lowest point at the James River near mile marker 60!! You will see a 3000 ft elevation change in 15 miles. Brakes and transmissions take a beating here if you are not familar with mountain driving. The speedlimit on the parkway is about 35 so plan on driving slow.  Also a few of the pull outs for sceinic overlooks are dead end and if you are pulling a trailer it's easy to get into trouble turning around.  However most overlooks are pull through and are no problem for any vehicle.  
This is a beautiful drive and you should not be intimidated by it. However good planing and knowledge is essential.