Audio plays with no animation and there are no FaceFX errors in the log
Make sure the character's Animation Blueprint is referenced in the Blueprint Class, the Blend FaceFX Animation Blueprint node is added to the Animation Blueprint, and it is connected properly.
My character's face explodes when playing an animation
Make sure the Compensate For Force Front XAxis setting on the FaceFX Blueprint Node matches the skeletal mesh import setting.
All other issues
Make sure there are no FaceFX warnings or errors in the log (launch the Unreal Editor with the -Log option).