1. He is an ear, nose and throat specialist.

2. He is an ears, nose and throat specialist.

(Do we have to use 'ear' or 'ears'?)

That type of specialist is called an ear, nose, and throat specialist. The plural is not used.

Sometimes it's abbreviated -- an ENT specialist:
http://www.google.com/search?q=ear+nose+throat+specialist+spring%2C+tx&rls=com.microsoft:en-us&ie=UTF-8&oe=UTF-8&startIndex=&startPage=1&rlz=1I7GGIE_en