While we do not have any official statistics on health problems in the Havanese, there is a great deal of autoimmune reactions and diseases. This is most likely because of the small number of dogs used to rebuild the Havanese after it was decimated during the Cuban revolution. However, world-wide we do have a great deal of diversity and so it is possible to bring genetic health, diversity, back to the Havanese.
This is an example of how the program can be used even if a breeder has no understanding of genetic principals:
http://www.sonrisashavanese.ca/diversity.html
To read more about the program and what has been discovered about the Havanese gene pool go here:
https://www.vgl.ucdavis.edu/services/dog/GeneticDiversityInHavanese.php