These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
The effect of "Stumbling" goes on a chain immediately after a monster is Summoned. As a mandatory Trigger Effect, "Stumbling" is always on the chain before optional Trigger Effects (“Mobius the Frost Monarch”) or chained Spell & Trap Cards (“Trap Hole”).
"Stumbling" changes a monster to face-up Defense Position, not face-down Defense Position.
When "Stumbling" and "Final Attack Orders" are both active, a Summoned monster is changed to Defense Position, then changed to Attack Position.
If "Stumbling" is in effect and you Summon "Exiled Force", and your opponent has "Trap Hole" Set, "Stumbling" initiates a chain with "Stumbling"'s effect as Step 1. Your opponent can activate "Trap Hole" as Step 2. You cannot chain "Exiled Force" because its effect is Spell Speed 1. Therefore "Trap Hole" will destroy "Exiled Force" before you have a chance to Tribute it.
If "Dream Clown" is Summoned while "Stumbling" is active, and changed to Defense Position by "Stumbling"'s effect, "Dream Clown"'s effect activates after "Stumbling"'s effect resolves.
Mentions in Other Rulings
Berserk Gorilla: If "Stumbling" and "Final Attack Orders" are both in play, and "Berserk Gorilla" is Summoned, "Berserk Gorilla" is destroyed when it is changed to Defense Position by "Stumbling".
Spirit of the Pharaoh: If you have "Stumbling" on the field and "Spirit of the Pharaoh" is Special Summoned, his effect can be activated but it is a chain with "Stumbling" as Step 1 and "Spirit of the Pharaoh" as Step 2.
Tragedy: You can activate "Tragedy" after an Attack Position monster is changed to Defense Position by a card effect, such as..."Stumbling".
Vanity's Call: Unless the activation of a card can be negated, the effect will not be negated either. So an effect like "Stumbling" on a chain will not be negated nor destroyed by "Vanity's Call".
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.