This is a guess as I haven't brought G3 into poser but maybe check the skinning method. It might be one version works better than others. Hopefully someone with more knowledge will be by soon with other suggestions.

Does it only do it in the Bullet Physics or does it do it in both Bullet Physics and the Pose room?

hborre it only happens in Bullet Physics and not in the normal Pose room.

The view on the top image makes me think you look at co-incident polygons, and the preview render engine having difficulties to make out which of the two is in front.

I do not know the exact implementation of Bullet in Poser but I would not be surprised if it involves adding an extra 'Bullet friendly' copy of geometry to do the computing on. 

How did you bring this G3 figure into Poser? I recall DSON also did make extra geometry.

This may cause a conflict. 

FVerbaas

I  first exported her from Daz3d software to blender. Then exported the blender version of her (as FBX version) to Poser. That way she can work in Poser without having to use Dson. When you bring a Daz G3-G8 character in Poser with Dson, they can't wok in Bullet Physics! So I FBX the character through Blender to Poser and it appears to work. However, the G3-G8 character has issues with the face (as seen in the top picture) when you do expressions after running the character through Bullet Physics. I was wondering is there something you can do in the setup room to seal her face and make it when she makes expressions her face won't break up (like most other characters)?

I believe Genesis 3 to Poser utility corrects the lack of expression problem but you need to use DSON to import the figures into Poser before applying the fix.  I can create a fully useable G3 and G8 figure by resaving a new .cr2 DSON import back to the Poser Library.  That is the other option to create a functional figure if you can get working.  I can but I haven't seen other users post their results.

hborre

The problem with bringing the G3-G8 through Dson is that once you get it (full functioning) in Poser with Dson it does not work in Bullet Physics. Every time  bring a Dson G3-G8 character into bullet physic, Poser crashes. So I've been bringing it through Blender (instead of Dson). Now, if you can make it work through Dson inside of Bullet perfectly with out crashing, that will also work for me. My goal is to get G3-G8 into Poser and be able to make them work with Bullet Physics (Softbody Dynamics).