Between when I wrote this post, and the next time I checked the issue to develop my work around, Google upgraded Chrome to 19, and the issue went away. These background updates are crazy.

In the current release of Google Chrome, when I edit a page, and click the Insert Image button, then Browse server, the window opens, but does not appear. I can get it to appear if I right-click on the window preview icon in the taskbar and Maximize the window, but this won't be an acceptable solution for my client.

The issue does not appear to happen in Firefox, Internet Explorer, or Chromium 14.

I might have a temporary fix for the issue that I can do, but this is an issue that might be best addressed upstream.