The most common problem I have with Echinacea is the Aster Yellows Disease which shows up occasionally in my garden. The above picture shows what it looks like as compared to a normal Echinacea.
The only solution to this is to dig out the entire plant and throw it away.
The second problem I have are Rosette Mites. They only affect the seed heads.
The main solution is to clip off the flower heads and get them out of your garden.
I found a great article on these two problems at this link.