There are two ways to play a non-raid without having to pay attention. The first way is a loot ticket, but I'd save those since they're pretty hard to get and become useful later. The other is the little Fast Forward button in the top right corner once you start playing. You can do this on quests, titan hits, or most anything that isn't a raid. WARNING!! The moves are RANDOM, so you better have a team that can handle the worst plays of all time!