The Duke describes the last Duchess as if she were wanton with her attention, inadequately class conscious and overly friendly. As rowens says, his primary complaint is that she does not treat him with more reverance or favour than she does anyone else. She loves everyone and everything: "she had a heart too soon made glad, too easily impressed". She enjoys life and people, and does not differentiate between nature and art, high or low class, men in general and her husband with the 900 year old name.
She is not a coarse woman--she blushes easily (too easily, according to the Duke, and too frequently as well). She smiles at everyone (friendly, but undifferentiatingly so), and she thanks everyone (this makes her too free with her gratitude). As far as the Duke is concerned, she should only be thankful to him for giving her his name (and title).
According to the Duke, she is oblivious to her faults, and does not correct herself (he doesn't tell her he sees anything wrong with her behaviour because that would be "stooping" and the Duke never stoops.
So her three greatest faults are that she is uncommonly friendly (which makes her common in the Duke's eyes), she is insufficiently grateful and subservient to the Duke, her husband and, finally, that having made these grave errors she does not see them and correct them on her own (thus putting the Duke in the uncomfortable position of feeling he must tutor his wife, which of course he cannot do).