My house smells musty, and my kids are always sneezing and complaining of watery eyes. What can be done to identify the source?

Musty odors are usually the result of mold growth. Mold growth is always the result of inappropriate moisture. This can come from a plumbing or roof leak, water getting into walls, or high humidity.
If health issues are a concern, air samples for total fungal spores or culturable samples may be collected to provide data to determine if the indoor environment is unusual when compared to the outside environment.