Question: I have moved into a house with a nice Wolf-range griddle, and I would like to know what the primary advantages of the griddle are over a cast-iron skillet, including, is there anything I can do with a griddle that can not be done with a skillet?

I have found that the primary downside to using the griddle is the time it takes to heat up, so when cooking for one, I would choose the skillet. The primary advantage of the griddle is that it provides a larger, easier cooking space. 

Am I missing other major advantages of having a griddle?

Answer: 
Yes, you don't have the edge of a pan in the way when going to flip things, but it also means that you don't have a mass of metal there to add as a heat sink, which can help dramatically when pre-heating your pans, as they'll be evenly heated across their bottom more quickly (at least, compared to something of the same material, such as a cast iron skillet)

More importantly, in my opinion, is that without the sides, you don't hold in moist air, so when cooking things like hash browns, you can get a better crust on 'em without steaming them.
I would say the biggest advantage, which you've hinted at, is being able to use a spatula for quick and easy flipping (think pancakes, french toast, etc). Apart from its shape and size, there really is no other difference (even the difference in heat-up time, I've found, is negligible).