I made the mistake of impatiently hitting the escape key (or function key or whatever) often enough to pop up the little round speech feedback window. I cannot for the life of me get the window to close now.
According to Apple's support page
if I "Turn off Speakable Items in Accessibility preferences", the window should close. It does not.
I tried making sure that Speakable Items was shut off, and then rebooted my computer. The pesky window appeared again.
Anyone have a clue how to get rid of the little monster? Minimizing it to the dock doesn't count---I want it closed.
For what it is worth, I noticed today that switching input methods from US keyboard to Spell Catcher (10.4.1) was causing the Speech Feedback window to open. Clicking on Input Menu > Use Speech Commands closed the window. [The Input Menu is the menu which Spell Catcher shows in the menubar; it also appears if there are multiple lanuages/keyboards set up in the Input Sources tab of the Language & Text preference pane.]
This appears to solve the problem I was having.