I'm no expert, in fact I've never made or textured a mesh. But it would only seem sensible to try ^^ In whatever you used to make (or convert) the mesh, make sure each part is seperated? Perhaps because it's all one blob rather than seperated into different layers, the texture doesn't know where else to go. Usually, in meshes with more than one texture, there will be an arrow next to the Material: box. Once clicked it shows the different textures used on the different parts of the mesh. Not sure if this helped at all, but it's all I could think of to try and look into.
Did you download the mesh from a website then convert it? Where did you get the model from?