You didn't provide much information on the model and texture(s), so I'll just go by what I know:
The model is most likely has multiple textures applied to each object so if you just drag a texture onto one, only the part of the object that the texture belongs to will be mapped correctly.
You know how you click the "vertices" button when you have a mesh selected to edit the vertices? Instead of that button, click the button on the far right. This will allow you to select elements. Now go through the mesh, select elements, and guess which texture belongs to that area. Then drag the texture into the selected area and check to make sure it looks right. If not, take another guess at what texture belongs there.
Continue this for every single other element of the object.
If there's only one texture though, that probably isn't the problem. Looking at the image though, you seem to have a least 6 textures for that model.
I don't think the UVs coordinates would be wrong, unless that program you exported the model from doesn't export them (which would be incredibly stupid)
