It was only one of the tree parts of the CDC test that was giving false positives in most cases. Also, the experts on This Week In Virology thought that the CDC was being too clever in how it designed its test and that's why it got into trouble but I don't feel qualified to try to explain why exactly.

A false positive in the case of corona virus shouldn't be a problem since you shouldn't seek medical treatment unless the symptoms become severe.

As others have said, it's a huge problem if it leads people to think they're now immune to the coronavirus.