The mystery thickens around the case of the black rectangle. Scott noticed that it comes up more frequently when there's a scrolling text banner at the bottom of the screen of the channel you're watching, so we think it means the TV thinks it's being communicated to. Basically, the black rectangle is its way of saying, "V-ger requires the information!"
However, things are further complicated by the fact that it came up while we were watching a DVD with the subtitles on: suddenly, there was the rectangle, and the subtitles were appearing inside it!
I did find something online suggesting that we accidentally punched the right buttons on the remote for the TV to go into programming mode, and the way around that is to unplug it for four hours to let it reset.
We'll try that.
Now let me exult about the weather for a moment. I woke up cold! Not just chilly! It feels like late October. I may have to extract the goosedown dyne from the back of the closet. Visions of jack-o'-lanterns dance in my head. I find myself dreaming of hearty CrockPot roasts and bowls of chunky stew. I dug out my toasty slippers when I got up and popped my icy feet happily into them. The cat was peeping pathetically in a very particular "Hey, it's cold!" kind of way when I got downstairs, too. Fall! Glorious fall.
Bring it on, I say.
May summer and its sweaty misery die an early death this year.
Update: I am updating this post several months later because I'm seeing several people hitting my blog via a Google search for what to do about the black rectangle on their TV screens. Answer: Your caption setting is on Text1 or Text2! Grab your remote, hit Menu, deselect the Text1 or Text2 caption setting, and you'll be rectangle-free. At least I was. Good luck!