1. Converted mana cost
Remember when I said that the characteristics of the face that's up are all that matter? That wasn't quite accurate. Under the new rules, the converted mana cost of the back face of a DFC is based on the mana cost of the front face. (Previously, because the back faces lacked mana costs, their converted mana costs were all 0.) The one exception is if something is a copy of the back face of a DFC, its converted mana cost is 0. So If I control Insidious Mist, it has no mana cost, but its converted mana cost is 4. If I then put a copy of Insidious Mist onto the battlefield, that copy's converted mana cost is 0.
2. Entering the battlefield transformed
A few effects can put a card onto the battlefield transformed. This means to put it on the battlefield with its back face up. Starting with this set, we have a new rule that if you're told to put a card that isn't a DFC onto the battlefield transformed, it just stays where it is. This may affect a few cards in this set, but I think the Magic Origins planeswalkers illustrate the change nicely. (This is code for "The cool cards in this set I could use to illustrate this haven't been previewed yet." I know. I feel the same way.) Say you control a Clone that's copying Jace, Vryn's Prodigy, and you activate faux-Jace's ability with four thousand cards in your graveyard. Well, four thousand is "five or more," so faux-Jace dutifully exiles himself. Then he tries to return transformed, but in exile he's just a single-faced Clone. He's not a DFC, so he gets detained at the border and remains in exile. I hope the card you drew was good, because this wasn't a great play otherwise.
3. No flippy-floppy
I've saved our most technical change for last. Here's the new rule: if a DFC has an activated or triggered ability that transforms it, that permanent transforms only if it hasn't since that ability was put on the stack. What does that mean? For example, say you activate Elusive Tormentor's ability, then you activate it again in response. Why? Because you want to discard a lot of cards. Why? We're almost there. Relax. The first ability to resolve will cause Elusive Tormentor to transform, as expected. But the second ability won't, as Elusive Tormentor has already transformed because of the first ability.