To fix the faces being oriented incorrectly, load the model into a 3D modeling program like Blender and flip the normals of the faces that aren't displaying correctly.
Three.js meshes have a doublesided property you can set which will usually allow you to display the model with the faces visible from both sides.
Here's a short example of how to load a collada mesh and enable double-sided rendering.
var loader = new THREE.ColladaLoader();
loader.load('path/to/mesh.dae', loadModel);
function loadModel(geom) {
var mesh = new THREE.Mesh(geom, new THREE.MeshBasicMaterial());
mesh.doublesided = true;
scene.add(mesh);
}
And a live example: http://jsfiddle.net/r7Yq2/