My dog has a faint heartworm positive. Is it serious? What's next?

A Light positive is still a positive. I would ask your vet to send out test to an outside Lab to confirm the results using a different type of test. You can also have an ultrasound done to see if your dog has any adult worms at this time. Your dog should currently be a heartworm preventative every month like Heartgard. Most heartworm tests are actually looking for antibodies in the bloodstream, so when they come up positive (even light positive, this means that your dog has antibodies or that your dog has been exposed. It may be that your dog doesn't have any adult worms of his/her own at this exact moment, but that he/she has baby heartworms floating around in the bloodstream because he/she is constantly being exposed to them (be it from another dog in the area who is infected and mosquitoes are passing it around or you live in a rural area where there are a lot of coyotes who are infected?? These are very far fetched reasons.. The most likely cause is that your dog is infected but has what we call a "low case load" and is producing a small amount of antibodies and therefore shows a light positive. Further testing will show you how advanced the disease is (like I said, ultrasound, xrays, etc) but regardless, you should treat your dog. One heartworm WILL eventually become two, three four etc. The longer the problem is left untreated, the worse it will become and the more damage they will will do to your dog's heart, lungs and overall health.