UDE has updated the FAQ and has clarified much on Divine Wrath.
WARNING THIS IS A LONG POST
DIVINE WRATH
You can activate the effect of "Divine Wrath" to a Flip Effect, Cost Effect, Trigger Effect, or Multi-Trigger Effect. But not to a Continuous Effect. This is because Continuous Effects cannot be chained to.
For example, you can chain "Divine Wrath" to the effects of "The Creator" (Cost Effect), "Fox Fire" when it is Special Summoned (Trigger Effect), "Strike Ninja" (Multi-Trigger Effect), and "Homunculus the Alchemic Being" (Cost Effect).
You can chain "Divine Wrath" when a Multi-Trigger Effect is activated to negate another card, such as "Horus the Black Flame Dragon LV8", "Sorcerer of Dark Magic", "Dark Paladin", "Maryokutai", and "A-Team: Trap Disposal Unit".
You cannot chain "Divine Wrath" to Continuous Effects such as: "Perfect Machine King", "Raging Flame Sprite" (either effect), "Jinzo", "Fire Princess", "Mad Sword Beast", "Hayabusa Knight", "Cat's Ear Tribe", "Amazoness Swords Woman", "Harpie Lady 3", "Fusilier Dragon the Dual-Mode Beast", "The Fiend Megacyber", "Blade Knight" (either effect), monsters that can attack directly (Toon Monsters, "Jinzo #7", etc.), or monsters like "Element Saurus" and "Shadow Ghoul" that gain ATK continuously.
You cannot activate "Divine Wrath" when "Giant Orc", "Goblin Attack Force", or "Spear Dragon" changes to Defense Position because these are considered Continuous Effects.
You can activate "Divine Wrath" in a chain to a Trigger Effect that activates when the Effect Monster is Summoned such as "Breaker the Magical Warrior", "Dark Magician of Chaos", or "Marauding Captain". The opponent must declare the activation of "Marauding Captain"'s effect before "Divine Wrath" can be activated. In this case, the monster that would have been Special Summoned remains in the opponent's hand.
You can activate "Divine Wrath" during the Damage Step because it is a Counter-Trap, so you may activate it to negate the effect of "D. D. Warrior Lady", "Reflect Bounder", "Injection Fairy Lily", "D. D. Crazy Beast" or "Mystical Knight of Jackal".
You can activate "Divine Wrath" against "Sasuke Samurai" or "Mystic Swordsman LV2" when they attack a face-down Defense Position monster.
You can activate "Divine Wrath" to negate either effect of "Don Zaloog" and to negate the effect of "Airknight Parshath" that allows its controller to draw a card.
You can activate "Divine Wrath" to negate an effect that activates in the Graveyard, such as "Witch of the Black Forest", "Mystic Tomato", "Despair from the Dark", "Night Assailant", "Electric Snake", and "Sangan".
You can activate "Divine Wrath" when the opponent discards "Kuriboh" from his / her hand to negate the effect of "Kuriboh", and when a "Night Assailant" is sent to the Graveyard to negate the effect of returning a Flip Effect monster to the owner's hand.
You can activate "Divine Wrath" when "Exiled Force", "Red-Eyes B. Chick", or "Paladin of White Dragon" is Tributed for its own effect, although you do not destroy the monster because it is already in the Graveyard.
You can activate "Divine Wrath" when "Dark Necrofear" returns from the Graveyard as an Equip Spell Card during the End Phase.
You can activate "Divine Wrath" when the opponent uses "Relinquished"'s effect to equip itself with a monster, or when "Relinquished"'s effect inflicts damage.
You can activate "Divine Wrath" when a Spirit Monster is returned to the owner's hand by its own effect, and the Spirit Monster will be destroyed and sent to the Graveyard.
You can activate "Divine Wrath" when "Lava Golem" does damage, but you cannot activate it when "Lava Golem" is Special Summoned.
You cannot activate "Divine Wrath" when an "XYZ" monster is Special Summoned because that is a condition of Summoning, not an effect.
You cannot activate "Divine Wrath" when a Fusion substitute monster such as "King of the Swamp" is used in a Fusion Summon, because that is a Continuous Effect.
You can activate "Divine Wrath" when any Union Monster activates its effect to equip itself to another monster, because that is a Cost Effect. However, you cannot activate "Divine Wrath" when a Union Monster Special Summons itself back as a monster, because that is an effect of an Equip Spell Card.
You can activate "Divine Wrath" when a "LV" monster is sent to the Graveyard to Special Summon the next level version (a Cost Effect), and "Divine Wrath" will negate that effect, even though it cannot destroy the "LV" monster because it is already in the Graveyard.
http://www.upperdeckentertainment.com/yugioh/faq_card_rulings.aspx?first=D&last=E