Sometimes the permanent teeth come in and the baby teeth do not fall out. This happens often with the canine teeth, or "fangs" (same name in both dogs and cats). Usually these retained baby teeth are extracted when the pet is spayed or neutered to avoid future dental problems.
If they are not extracted, food and debris can be caught between the teeth, leading to early decay, tooth loss or gum disease. The bite may be affected, thereby affecting the other teeth and gums. The teeth, by virtue of being so close, risk being weakened over time. This can lead to tooth loss or decay.
The retained baby teeth are not as large or as hard (mineralized) as the adult teeth and risk being broken during play or chewing, which can lead to pain or infection at the site.
In short, the retained teeth should be removed if they do not fall out on their own by 7 months of age. Most vets will check for retained teeth at the time of spay or neuter and remove the additional teeth for a small fee (or free, in some cases). If your pet is not scheduled to be spayed or neutered, please see your veterinarian to discuss the removal of any retained teeth before dental problems set in.
Dental Anatomy of Dogs