How to Complete A Fatal Mistake
Your objective is to destroy all the traps on the field within three rounds. The only way to do this is to step on them, OR, if you have Vaan in your clan, he can use the Salvage ability to turn the traps into loot.
The traps are not hidden; there are color-coded marks on the tiles that have traps. The green ones are Leech traps, which cause a small amount of damage, the yellow traps are Silence Gas, which causes silence, the blue ones are Sten Needle traps, which damage you for 1/2 your current HP, and the pink traps cause Charm.
If put any Seeq into battle, make sure that they are not using the "Avoid Traps" passive ability, because they won't be able to destroy the traps.
If you don't want your units to get Charmed, you can equip things like the Ruby Earring or the Ribbon to make some units immune to Charm.
Because of the layout of this location, you should consider using Gria because they can move around the field much more easily. You could also use a Chocobo Knight on a Black Chocobo, since they can fly, too. Time Mages and Jugglers that know Smile Toss can also help you complete this quest more quickly. And you could do the General Training and Teamwork Clan Trials to get the Speed↑ and Move↑ Clan Privileges, which could be helpful here.
The law forbids Targeting All Units. You probably shouldn't bother attacking the monsters unless they are really in your way, so you probably won't need to worry about this law. But if you do decide to attack the monsters, be sure not to use Scholars, Illusionists, or Tinkers, and don't summon Scions, because these all target all units (even though Illusionists only target enemy units, it still breaks this law). The Ranger Awareness ability also targets all units, but you won't need to use it because all the traps are already revealed at the start of the battle.