Advantages are clear that existence of some trusted third party guarantee than the component is trustworthy. Providing Trustworthiness means the system property that denotes the degree of user confidence that the system will behave as expected. The attributes of trustworthiness are availability, reliability, safety, and security.
Disadvantages: A certificate authority acts as a third party issuer that ensures the acceptance of the certificate. Certification authority typically requires a subscription to their services, which requires a monthly payments to continue the usage of the component and hence it becomes a cost factor.