If you have a model created from several objects or meshes, first make sure that each individual mesh is manifold (water-tight). You can tell this by going into edit mode, pressing A (once if any vertices are selected or twice otherwise) to select none, then hit ctrl-alt-shift-M (on a Mac it's ctrl-opt-shift-M).Prepping Blender Files for 3D Printing (via Beyond the Beyond)
Any vertices that get selected when you press that key combination are non-manifold vertices that have to be fixed. Often, fixing these is just a matter of creating new faces (F key) out of sets of 3 or 4 vertices. Sometimes these are stray vertices that are unattached to anything, or are attached to just one vertex by an edge. These can usually be deleted, unless they are intentional (such as those vertices uses to affect the shape while using a subsurf modifier), in which case you want to wait until after you've applied your modifier to delete them. Another possibility are vertices that are part of more than one overlapping faces...
Open the copy of the file, and select each object, one at a time. In object mode, apply all modifiers, then switch to Edit mode, hit A once or twice to select all vertices, then press ctrl-T to triangulate all faces. I don't know why, but Blender does a much better job with Boolean operations if the meshes are triangulated.
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