While the ability to be granted hearing is an overwhelming benefit a wearer of a cochlear implant has to accept the reality that they're broadcasting to the world that they have hearing difficulties. Beyond this there may be intimacy issues or difficulty obtaining romantic interests with such a device attached.
There are negatives to cochlear implants especially when they are implanted at a later age. Some adults have actually had their cochlear implants removed. It is too much of an adjustment for them and their lives. It can be overwhelming for them to sort out all these new sounds. When the implants are done in children, there are no negatives.
Cochlear implants are a great invention. There are practically no negatives to them that I can think of. A person who gets the implants can often hear for the first time in his or her life. The implants are also enabling deaf people to perform in conversations that include listening and talking.
While any medical devices comes with risks, I would say that cochlear implants offer far more pros, then they offer cons. The device may be annoying and a person can develop complications, but the device does offer a deaf person the ability to hear (or hear better). This can be vitally important for deaf children if they receive the implants before hitting a critical age in learning.