You can find all of the controller tricks listed here: http://na.finalfantasyxiv.com/lodestone/playguide/win/manual/
One thing that isn't in there though is Target Filtering. You can go to Character Settings > Control Settings > Filters > Filter Customization to turn on extra targeting modes. For instance, you can hold L1 and tap B to cycle through enemies only.
Actually I'm pretty sure it's the Sit button that does it. Because for me it's where I set it, on the right stick. And sometimes when I try to dismount in a hurry to join a FATE it doesn't work. I suspect it's because some mob is beating on me, and when you have a target selected that button will lock instead of sit. I'll have to test it some more.