Usually the first week of Feb is great. We usually go the first or second week, and we generally have had better luck with low crowds during the first week. The National Dace Comps are usually during that time. I believe the are coming in on Feb 1 for 2008. They usually stay at the All Star Resorts and Caribbean Beach. They really do not impact the park crowds too badly, but if they are staying at a resort that you are you will notice them.
Mardi Gras is Feb 5 for 2008. I haven't been there during Mardi Gras, but from reading other posts it seems like a lot of people from LA visit during this time since school is out. So, I am not familiar with crowds during Mardi Gras.