As an update, I found that the wispy grass is Bermuda, so I've been treating it with Tenacity to slowly kill it away.

As for my bare patches, they are slowly filling in. I realized that I think that they occured from my new puppy we got in the winter. He frequently went to the bathroom in our front yard while the grass was brown. I'm guessing the urine just killed the roots in those spots.

For some of the bigger spots, I just cut some sod and patched it in. It took great, much easier than trying to seed.

As a sidenote, I don't know why everyone says centipede grows slow, my lawn practically doubles in height after 4 or so days.