The default Reminders app changed a little when iOS 6 came about and the way you switch between lists was one of those changes. If you're the type that creates Reminders lists for different events, the importance of switching between lists quickly is probably pretty important to you. Many users were left wondering if Apple took this functionality away since they couldn't swipe across their lists like they used to.
As it turns out, Apple just changed up where you swipe...
Launch the Reminders app from the Home screen of your iPhone.
At the very top you'll see the name of the list you're currently in.
Opposed to swiping anywhere on the screen, swipe your finger left or right on the name of the list.
You'll notice that this allows you to swipe between lists again.
We aren't exactly sure why Apple changed this functionality but as it turns out, they didn't completely take it away. Just make sure you're swiping across the title of the list and you're good to go!