You can slide between the cards in the same way that you slide between homescreen pages. When you're on a card, double clicking the home button will bring up extra controls or information that is relevant to the card, if necessary. So when you're on the weather card and you double click the home button, the card will expand to show the weekly forecast.
Brentcas also wants to see a customizable grabber. Currently the lockscreen grabber only launches the camera.
When something has taken over the front card, though, it will also take over the app grabber. So if you're getting directions from the lock screen, the app grabber will bring you right back to that app.
Finally, brentcas suggests that apps should have access to heavy notifications that take over the user's screen.
Apps like Skype and Google+ should have just as much access to the lockscreen as the Phone or FaceTime apps. And to be clear, this wouldn't lead to confusion from the user or a process that isn't clean.
Check out a few screenshots below or hit the link for the full concept.