Split whiskers in cats and dogs generally are nothing to worry about. My pal Buster (pictured) gets them all the time.
Whiskers (technical term: vibrissae) are special, thickened hairs that function as sensory apparatuses. Whiskers help dogs and cats detect air movements, and help them identify solid structures in extremely dark conditions.
Whiskers, like all hair, are subject to the stress of everyday life. They occasionally break or split. They sometimes fall out.
When a whisker splits, I recommend doing nothing about it. Eventually the split whisker will be shed, and a new one will grow in its place.
It is true that certain diseases cause whiskers to become especially brittle and more likely to split or shed. These diseases usually have other symptoms as well–affected animals usually develop bald patches, or they may consume excess water or lose or gain weight.
However, if your pet simply has a few split whiskers with no other symptoms, I sincerely doubt that anything serious is going on.