I'm experiencing the same problem when using the 'insert media' button, although for me the problem only occurs with IE6 -- but it does affect all video file types, not just MPEG.
I've found that when using Cute Editor in IE6, sometimes the necessary <param> tags are generated by Cute Editor, but sometimes they are not (seemingly at random), and switching between Normal > HTML > Preview views before the form is submitted also immediately removes the <param> tags and prevents a video from displaying in IE. When using Cute Editor in IE7 or Firefox the tags are generated and retained as expected.
I can't recreate the problem on the Cute Editor demo page, but we are using much larger video files (eg. 2MB) than the tiny 'clock 'example AVI made available here -- don't know if this would make any difference?
Is this a bug, or a configuration issue? I've checked my configuration settings and can't find anything that would affect <param> tags between browsers in this way -- but any advice would be appreciated.