There's not much Cooper has done so far to mimic us.  I keep waving "hi" and "bye."  I even try some sign language at feeding times - more, all done, hungry?  I think he understands hungry, but only when I say it.  I tell him "mama" and "dada" all day long, only to get a loud shriek in return.  (Oh, he's got the shriek down pat - sometimes we have shrieking contests when it's just Cooper and me around.) I do think we caught him clapping a couple of times but not really in response to us.  
And then yesterday it happened - he started mimicking... THE DOG!  Yes, I caught him barking.  You may not believe me, so see for yourself.  It goes like this:  Cooper and I are playing upstairs.  All is quiet.  Roscoe begins barking.  Then I hear a faint "ah ah ah ah ah" from Cooper.  Over and over and louder and louder until Roscoe stops.  I think, "well that's unusual.  Surely he's not doing that because of the barking."  But then it happens again.  10 minutes of silence from Cooper and all of a sudden Roscoe starts barking. And so does Cooper.  Huh.  What do you think?  World's cutest barking baby?  I think yes.  :)