I've been playing Moira off and on on Quick Play, and I think I'm getting the hang of her. I still favor Zenyatta over her as my Support pick for Comp, but I think I have a better grasp on her than I do on Mercy or Ana.

Some Misc. thoughts/tips on Moira that I've picked up:
  • Moira seems to have problems with most DPS-centric comps, but she does wonders with a good Tank soaking/blocking damage so that your healing dot can do it's work.
  • Speaking of, apparently Moira's primary heal has a healing dot on it. It's a Healing Flamethrower! And much like a flamethrower, don't waste your resource by holding down until your teammate is topped off, just a puff or two is fine.
  • Furthermore, there is only so much healing you can do by holding down the primary over your team when they're taking heavy fire, so supplement it with the Healing Orb.
  • I'm trying to curb off of a bad habit of using vanish to throw myself onto a teammate in danger, only to get caught in the crossfire. Instead, throw a healing orb to your far off teammate, and save Vanish for Roadhog Hook, Genji Ult, etc. Vanish is an excellent escape tool since it gives the enemy team no cues as to which direction you went.
  • Moira's Ultimate is an okay but not great healing ult, and a pretty meh damage Ult. It's only when you can take advantage of both damage and the healing power that it becomes a great initiation tool.