Sorry for the late response.
What codec is the screencast footage? Does it look okay in FCP? How are you exporting it?
If you’re exporting to the DV codec and opening the file in QT, it will look horrible unless you enable High Quality video. (Apple+J, select video track, select visual settings, select high quality video)
If you answer the other questions, we might be able to give you some more input.
-Russ