Weird Blender Subsurface glitch For some reason, when I add the Subdvision Surface modifier, I'm getting this. Does anyone know what might be causing this?
Subdivision surface only works well with quads, and from the looks of it your model isn't constructed in the most clean way. There are a few things you can try short of remodelling the mesh:


Remove doubles
Recalculate Normals
Add a bevel modifier, which might be able to clean up the edges for you so you can apply a subsurface modifier.
Add 2 edge loops around the perimeter of the object so that subdivision works better.