I would like to suggest that when we are targeting and/or focus-targeting an enemy, our DoTs and Debuffs are the first to be shown. I can't tell you the number of times I couldn't see my DoTs on a boss during a FATE, 24-man raid, or high-level as a BRD or SCH/SMN.

I think the order should be:
Enemy Buffs and Fight Mechanics > Our Debuffs > Our DoTs > Other's Debuffs > Other's DoTs