Once in a while when i apply a pose to Genesis 1, especially when there's another character in the scene, it breaks apart the hands, fingers, and arm. Sometimes this is fixable by restoring the element, but in some cases, as with my Rhino character, that doesn't fix the issue. Has anyone else had this problem, and does anyone know how to fix it or what causes it? Here's a screenshot of what i mean. Look at his fingers:

I'm using Poser Pro 2012 SR3.1

I haven't seen this problem when I work with Genesis but I haven't used any of the creature morphs on a regular basis.  Are the poses designed for Genesis or are they universally applied from another model?  It almost sounds like a cross-talk problem if another figure is present in the scene.  You could pose Genesis in a separate scene and delete all background props and lighting after posing.  Save the scene.  Go back to the original scene you're developing and import Genesis from the saved scene.  This might work.  Now I haven't tried saving scenes within Poser and adding them to existing sets from the Library.  I think this might work also.

I wonder if the joint centre ERC is cross-talking? So that the joint centres are those for an unmorphed, or less radically morphed, figure instead of the Genesis in question. If you can reproduce it reliably please report it to DAZ by opening a Tech Support ticket with instructions.

hborre: The poses are for Freak 5. In the past, i've used a few M4 poses, and those usually worked on my other Genesis characters, though sometimes the feet break apart. But those i fixed by restoring the elements on them. But on the rhino, even after restoring elements, it breaks apart when i pose it. Also happens if i load a saved Genesis pose.  

RHaseltine: It seems kinda random. It doesn't happen a lot luckily, but when it does, it gets pretty annoying.

Is "Use Limits" possibly checked?  If so, try unchecking it...

The Use Limits feature has been known to cause problems with poses, if this is the case.  IIRC, there is a No Limits python script written specifically for Genesis/Genesis2 which fixes that problem.  It may be found @ sharecg.com.