Two issues I see there.
1) The red parts are where the model has no texture. This will require a reconversion to fix, but first you'll probably have to reapply the missing texture to the parts it was assigned to in TS.
I've had this happen with TS occasionally, still don't know why it does it, but TS will lose a texture and then not tell you. It'll appear correctly in TS until you try and sample it using the eyedropper. :\
2) The black and totally missing parts (ie, everything else) is where modview has found the texture, but it can't display it. At this time, modview only supports 256-colour .PCX files. If your images are any other type or colour depth, they'll not display.
If you want modview to display the textures, you'll need to make 256 colour PCX versions of all of them. Be careful not to let these files interfere with your main FS2 install, since they'll be lower quality and less efficient than the DDS versions you should use in-game. What I recommend is creating a folder structure like "ModviewTextures\data\maps" and putting the textures in there. Then manually configure modviews FS2 installation directory to be the "ModviewTextures" folder and it should read the files properly.
Oh, and also: to get maximum efficiency out of the engine, your models need to have as few textures as possible. Taylor has an excellent guide posted here:
http://www.hard-light.net/forums/index.php/topic,37158.0.html
