What I am seeing is a single wire coming off a 20AMP circuit breaker that is then capped with two wires(branch circuits) going to different locations. I have never had a problem but I am selling my house and an inspector raised the issue. Is this a real problem?

That's not a pigtail. That is just a splice. Technically, the splice should be in a junction box, not exposed. Then if something should happen, the fire is contained in the box.