Are these conflicts related to the same issue you reported in your other post? Same folder or different folder. Are the conflicts on the Home or Work PC?
In any event, since I asked you to capture the logs for your other problem, please attach them to another bug submission for this problem. You may want to only submit the logs from the machine with the conflicts showing in this case.
How to Submit Bugs and Live Mesh Logs
-steve
Microsoft MVP Windows Live / Windows Live OneCare & Live Mesh Forum Moderator