Thanks for the thought, azaozz. Here's an update. First, all 8 sites are working this way; it's something common...
Here's what I've tried. I went into my main site and deactivated all the plugins. Then I cleared caches and closed the browser. Next I went into the site again. Because I had the plugins deactivated, very little worked; I went through the /wp-login script and got back to the console.
I opened the editor. Still showing 2 tabs, with the HTML code showing on the Visual tab. The HTML tab was present but inactive. Attempting to click it did nothing.
I moved to the admin user page and unchecked the "Use Visual Editor" box to deactivate. I moved back to the editor, and the tabs were gone, as expected. So I reactivated the Visual Editor, and again, the two tabs were showing but only the Visual part was active. And the editor shows only the HTML when I look at a page or post.
Because I've got all the plugins deactivated, it can't be any of those causing the problem. Sure enough, there's no change in the editor behavior when I reactivate the plugins.
I tried this on 4 of my 8 sites. All of them give the same behavior. All of them were fine before the upgrade to WP 2.6.
I'm very confused. However, if I have to have only one view of the information, I'd prefer the HTML; I can hack my way through that okay.
Anybody else seeing this in their upgrades? I'd hate to revert all 8 sites at this point, just to get a better editor. (In fact, I won't; I use a separate blog editor for most of the work, only need the internal editor for touchups and such.)
DTR