As I thought about it, I decided that the most efficient route would be the one that maximizes mowing time and minimizes going over the same spots twice. Sharp turns (especially 180 degree turns) will lead to down time. But there is a balance there with going over the same areas more once. Trees and landscaping make it even more interesting.
So, I think the problem is actually an interesting one but I've never remembered to look it up when I get inside...until now!
For your reading pleasure, I present to you a thorough discussion of "the lawn mower algorithm"
If that wasn't enough, I somehow found myself on this related topic as well:
Mow your yard with lasers!
And finally, to the single image that made it all worth while: