The REST API does not allow direct access to all actions.

/todos.xml contains only active items. No access is available to deferred or completed items. These items can be found if you dig for them specifically by searching sequentially for todos/{number}.xml, but this is somewhat tedious.
It is undesirable to modify the existing /todos.xml as this would cause problems for existing apps.

Secondarily, todos.xml is a very heavyweight file. It contains the full content of every active todo. This is not suitable for incremental update of a synchronized database as would be appropriate for a mobile app.

Proposed solution:
Add several "index" feeds.
/todos/active.xml
/todos/deferred.xml
/todos/complete.xml

The union of these three feeds will allow REST API access to all current todos.

Each feed should contain only the ID and updated-at field for todos of the matching types.
The reduced content in these feeds will allow a client to download the full set of open todo IDs and then look at the updated-at times and pull only the specific todos which have actually changed since the last synchronization of the remote app.

Finally, it may be desirable to amend the REST API documentation slightly to document the life cycle of a todo.
Are todos IDs guaranteed to be assigned in increasing numerical order?
Are they guaranteed to be created without gaps in the sequence?
Under what conditions is a ID retired or removed from the set once it has been created?