What DIVX codec version are you using and what audio compression format is used in your file?
http://www.divx.com/en/software/mac/player (I don't have this installed on my home computer, but I can maybe reply to this posting tomorrow morning after I see what codecs it reports it can playback, apparently one of them is 3ivx encoded MP-4 files on 10.7.1)
Do edited projects using such files as you describe export properly.
Yes, I am able to Export Movie..., Share to Media Browser, Export using QuickTime, etc. No glitches, no missing still images, no missing audio, no stutters on playback. The only thing it won't do is allow me to change the speed faster/slower without first converting the clip that's the only outward visible sign that this isn't a Apple Intermediate Coded format .mov file. So I'm guessing that it's an h.264/MP4 which is edit compatible with iMovie, but it doesn't have any native capability to play it back with out the DivX QuickTime Component installed under 10.7.1.
I know this isn't quite a sample, but I think I can post the raw AVI file up on a webserver where you can pull it down if needed.