Mesh model has texture on all faces when in world.

[steph Arnott]

The texture has to be UV wrapped in Blender.

[steph Arnott]

The texture has to be UV wrapped in Blender.

[Rolig Loon]

So, did you unwrap your model in Blender and make a UV map?  Without a UV map, there's no way to know how textures will be placed on the model.

Did you apply different materials to appropriate collections of faces on the model? You can use up to 8 materials on models to be uploaded to SL.  If you haven't defined separate materials, then the same texture will apply to all faces.