Question about One

Recently I was listened to a podcast. During the program the host said "Well, let's now move on to the quick tips and jokers sections" and the co-host replied "Oh! I have been waiting for this one". My question is about the second sentence. If the co-host had been said "I have been waiting for this" without the word "one", have been the sentence wrong or incomplete?

To answer your question:

No, it would not have been incorrect to leave out "one."  By saying "this" he already stated that he had an expectation of that object.  Saying "one" is just adding extra emphasis to the idea that he had been waiting for that specific thing, but it was not needed.