Yorkies can be yappy.
They can be snappy.
They can be hard to train.
In fact, my Yorkie is all of those things and she is the best dog ever.
With these "problems" (which can be trained out to some extenet) comes a lot of personality. I have been around quite a few dogs and I'll tell you, Ellie is so spunky compared to them. I have never seen a dog with so much personality.
They do have lots of health problems but buying from a reputable breeder should help eliminate the risks. I didn't know better and now Ellie is on Denosyl for high bile acids. So they can be very expensive and they can be hard to train but if you find the right one for you, you won't regret it.