Somewhere in the transfer from FCP to QT, my video image acquires 7 grey rectangles, 3 on each side of the frame, and one in the center. Can anyone help me stop this ?

Maybe, but we'll need much more information. What format is your source footage? What format is your timeline? How are you exporting from Final Cut? What precisely do these grey rectangles look like? Can you post a still?

Frame with strange artifacts

I posted a frame on the blog above. (Couldn't figure out how to attach it here.)
I am running FCP 5.1.4 on OS 10.4.11. My footage is DVCPro HD, shot with an HVX200.
This thing happens with both 1080i and 720p footage. I am pretty careful to match up the sequence settings with the capture settings. (If something has to render, then I know I've made a mistake, so I go back and correct it before going on.)
The problem has been coming up when I import footage into Motion, manipulate it, and then export to a QT movie. I have just discovered that the problem doesn't arise if I export using the compressor, matching the settings (720p24 for example).
Any ideas on this would be greatly appreciated.

I don't have an answer but a couple of things - one, that pic in your blog doesn't show, so we can't see it. Two, here is how to post images to the forum : How to Post a Screen Capture and three - what you are describing sounds very much like what I have seen on an external monitor when it loses connection with FCP. One machine in particular I have seen this on did it for ages, until I trashed the preferences, which cleaned it up.