Your guys' comments have made me into a better caster in just one week. I really appreciate the advice. I'm still not doing a perfect job of line management, but I'm better than I was a couple of weeks ago. My casting is getting tighter too, except when I get excited and forget what I'm supposed to do.
I think I need a new rod, too. I got my rod before I knew how to cast, and I think that they gave me one where the guides are not lined up with the spine. Why do I say this? Well, I'm thinking of building my own rod and I've learned how to find the spine of a rod. On my rod, the guides are offset about 30 degrees from the spine. I've noticed that when I cast the rod has a tendency to twist in my hand, and I think that that explains it. I've started holding my rod off-center, with the reel and the guides splayed out a little bit to one side, so that the spine of the rod is lined up with the force of the cast, and my casts are straighter as a result.
The main thing I'm focusing on now is throwing tight loops. I don't do it all the time, but at least I know that I should be! It's weird, I notice that if I just focus on throwing a tight loop on the forward cast, the line goes farther than if I try to power the cast. I still have to put some force into it, though.
I'm casting well enough to catch fish, anyway. Went to the local canal today and got three huge carp under a mulberry tree, on a little bit of red deer hair that I spun to look like a mulberry. Then I caught a few little smallmouths on a yellow and black deer hair bug. I'm having fun anyway, which will keep me at it.
Thanks for all your help.