How to easily clean up or refinish cheap top coat on hardwood?
There could be a few different reasons for your situation.  I would lean towards the theory that only one coat of finish, urethane or maybe varnish was applied to a poorly prepared surface.  I'm afraid there is not quick fix to your problem.  I would be looking at stripping and sanding the entire floor, clean away every spec of dust and refinish with at least 3 coats of high grade urethane.  The surface MUST be lightly buff sanded and cleaned between each coat to give you a professional looking finish. It is a lot of work, but the results will be worth it.