They should not be persistent or be stacked, as they are above other elements on screen. http://www.google.com/design/spec/components/snackbars-toasts.html#snackbars-toasts-usage
While this makes sense from an UX perspective it would be nice as a developer to be certain that all toasts are eventually shown to the user and none is being skipped. We achieved this by wrapping $mdToast within a custom Notification service that takes care of delaying multiple triggered toasts.
On top of that the code below also takes care of a problem we run into when the same message was shown multiple times (showing a generic error message in a $http interceptor in case of a communication error). The toast is shown only once if the message is the same and it was triggered within a small time frame. Demo can be found here.