I recently purchased a bi-level home with two full baths. The inspection didn't include ductwork, but it seems to me that the downstairs bathroom is somehow venting into the rest of the house. There is a very large vent in our upstairs hallway, and when someone is going #2 downstairs, the smell upstairs becomes pretty strong as long as the exhaust fan is left on. It seems to be coming directly from the hallway vent. It's very unpleasant and definitely something we want to fix. The exhaust fan downstairs is very old and very noisy -- is it possible that simply replacing the fan might solve this problem?
If the downstairs fan is vented into the upstairs, replacing the fan will not do anything.
In order to determine where the fan vents from the bathroom you will need to find a way to trace the ductwork from the fan to it's exit point. A camera probe can help with this, or if it's a short enough run you might even try a flashlight and a 2nd person looking at the hall vent to see if they see the light.
If the vent is confirmed to be venting inside the house the only way to correct this is to open the walls/ceiling of the bathroom in question and re-run the ductwork. Something that should be done as the point of the fan is to remove moisture from the bathroom (not smells although that's a secondary benefit) and get it out of the house to reduce mold risk.