Hmm. By your description, I can think of a few possibilties:
1. Perhaps you just didn't import the OBJ's correctly. If that's the case, I'd say just give it another try.
-OR-
2. You might have somehow somehow gotten your normals reversed. I'm not quite sure how that could have happened accidentally, though. But if it did, the results would look like one possible interpretation of what you've written here.
If reversed normals are the issue, you'll need to flip them in a 3D modeling program. (Or if you understand the formatting that OBJ files are written in, and you're a masochist, you can reverse the normals by editing the text in the file directly.)
-OR-
3. If you're using the mannequin files straight from LL, be aware that some of them require cleanup before they're usable. A couple of them come with locked normals, which give the polygons a sort of black/gray gradient, faceted look. This doesn't quite fit your written description, but it's close.
If it is indeed locked normals what you're talking about, that doesn't have anything to do with Photoshop directly, just so you know. It's not an uncommon issue in polygonal modeling. (In most cases, it's the fault of the artist who created the model.) In any full-featured modeling program, when you encounter locked normals, you simply unlock them. But since Photoshop is NOT a modeling program, it's powerless to do that. It just displays whatever it's given.
So you've basically got three choices for those messy OBJ's. Bring them into a 3D modeling program and clean them up, use other ones that are already clean, or again, if you understand OBJ text, and you've got time on your hands, you can edit the text directly.
As for why those mannequin models have locked normals in the first place, your guess is as good as mine. I've always assumed it's got something to do with Poser, since Poser seems to be the only program capable of displaying them properly without first unlocking the normals by hand.
In any case, I'd recommend using Robin's OBJ's. They're all geometrically correct, and they've got her templates right on them.
http://www.robinwood.com/Catalog/Technical/SL-Tuts/SLDownloads/Exported_CS3_Avatars.zip-OR-
4. Another possibility could be just that you put a semi-transparent texture on one or more of your materials. Depending on your graphics hardware and drivers, that could potentially cause problems. If that's the case, just put an opaque background layer in each of your materials, and the display issues should clear up right away.
-OR-
5. It could be a driver issue. Try turning off 3D acceleration. (Edit -> Preferences -> Performance -> GPU Settings) If the problem goes away, then you know it had something to do with your graphics card.
If none of that does it, then I'm stumped for now. What I can say with certainty is that you shouldn't let the problem, whatever it is, color your judgment about how well PS does or doesn't handle 3D. Yours is the first report I've heard of any problems like this. Whatever's going on, I'm sure it's fixable.