This is what your home screen will look like after you've been sent multiple broadcasts:
To dismiss a broadcast from the home screen without opening it, swipe down. This swipe down action will remove the broadcast from your home screen. You will still be able to view it later from your inbox.
In your inbox, you will see a blue dot next to dismissed or unread broadcasts.
Mark a Broadcast as Read:
To mark as read, click the pink "mark as read" button in the bottom right corner of the broadcast. This broadcast will still be available in your inbox, but will not show the blue dot next to it.