I noticed that you have normal and specular maps in your models, however whenever I see your screenshots, they don't seem to have any of them,
so I decided to check their materials, and I found out that they were not using the correct shaders which is why they do not show.
Here is a comparison of how this would look if assigned properly. You should use mesh_color_unit instead mesh_color as your vertex shader (vs).
Pixel shader (ps) will vary depending on what textures you will be using, mesh_color_unit if it only has a diffuse and normal map,
if you have a specular map, it should be mesh_color_unit_spec, and so on (play around with it a bit, you can check, game/core/shaders to see what vertex/pixel shaders are available in HoN.
The _SP file should be set as specular not gloss, your texture is a bit dark, most models in HoN use vDiffuseColor="1.0000 1.0000 1.0000" and fSpecularLevel="1.0000".

As for bugs, it seems that you exported the model with the bones shown (left eye has it showing),
when exporting the .model file, be sure to hide the bones first, but keep the reference/effects/attachment bones shown.
Anyway, here are my material settings for the above screenshot.
Body.material
Code:
<?xml version="1.0" encoding="UTF-8"?>
<material>
<parameters vDiffuseColor="1.0000 1.0000 1.0000" fSpecularLevel="1.0000" fGlossiness="56" fOpacity="1.0000" fReflect="1.0000" />
<phase name="shadow" vs="mesh_shadow" ps="mesh_shadow" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="false" cull="CULL_BACK" />
<phase name="depth" vs="mesh_depth" ps="mesh_depth" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="false" cull="CULL_BACK" />
<phase name="color" vs="mesh_color_unit" ps="mesh_color_unit_spec" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="false" cull="CULL_BACK" layer="0">
<sampler name="diffuse" texture="BatmanArmoured_Body_D.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
<sampler name="normalmap" texture="BatmanArmoured_Body_N.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
<sampler name="specular" texture="BatmanArmoured_Body_SP.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
</phase>
<phase name="fade" vs="mesh_depth" ps="mesh_depth" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="true" cull="CULL_BACK" layer="0" colorwrite="false" alphawrite="false" depthwrite="true">
<multipass vs="mesh_color_unit" ps="mesh_color_unit_spec" srcblend="BLEND_SRC_ALPHA" dstblend="BLEND_ONE_MINUS_SRC_ALPHA" translucent="true" cull="CULL_BACK" alphatest="false" layer="0">
<sampler name="diffuse" texture="BatmanArmoured_Body_D.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
<sampler name="normalmap" texture="BatmanArmoured_Body_N.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
<sampler name="specular" texture="BatmanArmoured_Body_SP.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
</multipass>
</phase>
</material>
Head-Legs.material
Code:
<?xml version="1.0" encoding="UTF-8"?>
<material>
<parameters vDiffuseColor="1.0000 1.0000 1.0000" fSpecularLevel="1.0000" fGlossiness="56" fOpacity="1.0000" fReflect="1.0000" />
<phase name="shadow" vs="mesh_shadow" ps="mesh_shadow" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="false" cull="CULL_BACK" />
<phase name="depth" vs="mesh_depth" ps="mesh_depth" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="false" cull="CULL_BACK" />
<phase name="color" vs="mesh_color_unit" ps="mesh_color_unit" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="false" cull="CULL_BACK" layer="0">
<sampler name="diffuse" texture="BatmanArmoured_Head_D.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
<sampler name="normalmap" texture="BatmanArmoured_Head_N.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
</phase>
<phase name="fade" vs="mesh_depth" ps="mesh_depth" srcblend="BLEND_ONE" dstblend="BLEND_ZERO" translucent="true" cull="CULL_BACK" layer="0" colorwrite="false" alphawrite="false" depthwrite="true">
<multipass vs="mesh_color_unit" ps="mesh_color_unit" srcblend="BLEND_SRC_ALPHA" dstblend="BLEND_ONE_MINUS_SRC_ALPHA" translucent="true" cull="CULL_BACK" alphatest="false" layer="0">
<sampler name="diffuse" texture="BatmanArmoured_Head_D.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
<sampler name="normalmap" texture="BatmanArmoured_Head_N.tga" repeat_u="true" repeat_v="true" scale_u="1.0000" scale_v="1.0000" fps="15" mipmaps="true" fullquality="false" nocompress="false" filtering="true" border="false" />
</multipass>
</phase>
</material>
As for Eyes.material and Batarang.material, they are using the same settings as Head-Legs.material, since they only use diffuse/normal map.
Of course this could still be tweaked, fGlossiness="?", anyway, I'm too lazy to do that, I used the same value for all the materials.
Claptrap could also use some material tweaking.