You can use the "Reset" option to change accounts in the app. Go to Settings, then Reset, then tap "Erase All Content and Settings". You will then be prompted for your username and password again.

This process does erase all information for your account on the iPad, so be sure that you perform a sync before doing this.

Hope that helps!

I thought about trying this, but it wasn't clear whether resetting the app might inadvertently delete lists and tasks on the website. So I'm safe there -- it won't delete any online content?

Correct, using the Reset function of the app will only delete data stored on your device. All your tasks will remain available online or on any other platforms you are syncing with.

Hope that helps!

You also cannot log out so your lists pop up when you start the app. This needs to be fixed. I have asked RTM for the answer to this but suspect log out is not yet available.

lcholman,
Similar to switching user accounts, you can use the Reset function to remove your data (including your user data) from the app. The next time the app is started, you will be prompted for your username and password instead of having your lists displayed.