What methods exist for filtering air to alleviate allergies?
If mold is an issue in your house I'm not sure a furnace filter is really going to help, even a HEPA filter as all it will do is filter the air passing through the filter; it won't do anything to prevent the mold spores from entering the air where they are growing.

Generally the best solution to mold issues is to solve the moisture issue.  If you have any leaks (roof, pipes, etc.) then you need to fix those otherwise you'll never stop the mold growth.

If it is caused by high humidity then a dehumidifier would probably be a good investment.   Air conditioners dehumidify as part of their operation, so if you don't already have one it might be worth looking into adding one, alternatively if you already have one and it's not doing enough, a stand-alone dehumidifier can be used.