I took a look at the mesh with what I had. (Thanks for the link, WandW!)

I didn't see any obvious normal issues or winding order problems. I can't check the winding order outside of Poser with what I have with me atm. Winding order problems should be immediately evident in Poser's Preview window, since it uses OpenGL to render and OpenGL ONLY uses winding order to render normals. (I guess they do something tricky with the camera to switch backfacing poly material to "visible" in the Preview pane from the Materials Room.) I didn't see Poser's OpenGL Preview window balking at anything significant in the model and it should have if winding orders were reversed/mangled in spots. ("Should" have.)

However, the faces that should be coplaner are not coplaner. That means that the big flat area made up of large, long, tris contains tris that are not "flat", relative to each other and they do not share the same planar space on the Z axis. Meaning... "bent" faces on the group of tris. Simply put - The tris next to each other do not create a "flat" surface, even if they are not nonplanar, themselves, and are intended to create a flat surface as a group.

Why is this? It's likely that the logo was produced by converting a graphic to something like an Illustrator file, then either using that in a Boolean or just using it directly, then simply connecting the bounding edges of that construct to the sides of the box, making an interior surface with an embossed logo. But, the original 3D logo, itself, had the outer set of edges nonplanar relative to themselves on the z axis, so a consistent, coplanar, flat, extruded surface could not be created. (A guess only.) It's not bad at all, considering how finicky that sort of thing can be, depending upon the quality of the original image used, but the faces that are supposed to represent a flat (coplanar) surface end up not producing a flat surface. (If this was in quads, I'd love the model. But, it's not. :(  Still, it ain't bad at all for a freebie. I like the choice for the model. Very cool.) When extruding multiple edges, if those edges are not coplanar (Sharing the same location on the plane that you are extruding to) this is what happens.

So, the result is that the flat surface is bumpy (irregular) in spots. These inconsistencies are magnified between two faces the further one travels away from an edge, since these are tris and there's only one other point to play with. I could not really get a good look at the artifacts that the materials created in the original image. However, I would guess that this is a factor of two things: Faces that are not coplanar with their neighbors, when they should be, and the model being made up of tris, which plays heck with Poser.

How to fix: Make the tris that make up the flat surface of the interior actually "flat" by making them coplanar to one another where they should be. (The lid is not modeled at 90 deg, so rotation of the lid or resetting a tool's axis values relative to the lid will be necessary to easily adjust non-coplaner facets.) Do the same for the tris making up the deepest inset parts of the lid. Flatten (reduce the z-axis differences between faces in those groups to zero) and then move each one of those groups until you get a nice depth without mangling the bordering faces too horribly. Tidy up the bordering faces as necessary. Remap the object so that you can use a separate material for the deepest part of the "floor" of the inset logo, the "walls" of the inset logo and the flat portion of the inside of the lid "border" ing the logo. (Gives you something more to work with to really get a good contrast and "might" help Poser/Materials find some edges, there.)

PS - Disclaimer: This is a just a handwavy opinion from a few minutes of SWAG'ing the model. I could easily be wrong about the primary causes.