Let's assume I have a device that has both client and server applications running on it at the same time. The client application for example connects to a remote secure webserver (HTTPS) that requires client-side authentication. The device also offers an own secuer webserver (HTTPS).
I'm planning to use the same certificate for client-side authentication and for the device's secure webserver as this approach only requires having one private key. Is there any disadvantage in regard to security when the same certificate is used for both use-cases?