I had the problem where I just wanted to share common to-do tasks with my wife using the RTM Android app. Once I created a task in my Inbox, I was frustrated because I couldn't share the new task using the app, so we could both see the task that we needed to complete (e.g., grocery shopping list).

Since contacting support, I discovered that the best way to share things using RTM for Android is to log on via your computer and create a new list (call it "Shared To-Do" or "Grocery List," or whatever) and shared the entire list between you and the other individual, so no matter who puts something in that list, it will show up on both of our phones.

In order to make sure you are seeing that new shared list when you access the Android app, all you need to do is set the "Shared To-Do" list (or "Grocery List," etc.) as the default list on your phone and it will be the first list to come up. In case you need a refresher, just go into RTM on your phone, and touch MENU -> MORE -> SETTINGS -> TASKS -> DEFAULT LIST and select "Shared To-Do".