Telangiectasias are annoying abnormal blood vessels that become wider (dilate with blood). They are visible because they reside near the skin, but don't become apparent until they become engorged. Telangiectasias are not really a disease per se, but rather a sign of other diseases going on. You mother's rosacea is a prime example. So to answer your question, the spots are not serious in the sense that they could be life threatening. They are simply just annoying, and can make people self conscious especially when they show up on the face. Thus some people choose to get them evaluated and treated. The best type of physician for your mother to see about this issue is a dermatologist
. He or she can take a close look at the lesions and determine for sure if they are in fact telangiectasias. From there, you can discuss treatment. The first step will be to get your mother's rosacea under control. The dermatologist can review the medications she is taking and make any necessary modifications. Treatment for the telangiectasias can be tricky, but the most widely used therapy is called sclerotherapy. This is where a medication is injected into the veins causing them to shrink up and become invisible. I hope this turns out well for your mother. Good luck.