Some tips to have a healthy Periscope experience:
1.- You can block spammers, not only the broadcaster, but the viewer. Just tap the nick-name of the person you don’t want to see their messages and hit Block user. Voilá!
2.- You can hide the Chat if you want to see the whole thing: Just swipe to the right and you will see a Hide Chat button/link/text. Tap that one and done. You can see the broadcast at its best.
3.- Maps location zoom: You can expand the map of the location of the broadcaster if you want to zoom in. Just double tap the map and you’re good to go!