Too easily impressed: she liked whate’er She looked on, and her looks went everywhere. (23-24)
The Duke’s assessment of the Duchess is that she likes everything in the same way indiscriminately. As a connoisseur and collector, he values the ability to make fine distinctions between the quality of different objects or acts. The Duchess's general appreciation of everything – and everyone – in the same way frustrates him to no end. It’s important to notice that part of his objection to her behavior is that she isn’t critical or analytic about things the way he is.
There she stands As if alive. (46-47)
This is a simple but deceptive statement, which emphasizes several things including: the lifelike quality of the painting, the fact that the Duchess is no longer alive, and the idea that Frà Pandolf’s painting might replace the real-life Duchess for the Duke.
Notice Neptune, though, Taming a sea-horse, thought a rarity, Which Claus of Innsbruck cast in bronze for me! (54-56)
At the end of the poem, the Duke concludes his monologue by pointing out one more art object in his gallery – a statue of Neptune, the god of the sea, taming a seahorse. It’s important to him to emphasize the name of the artist and that the piece was commissioned especially for him. (Notice his use of the exclamation point, a rare occurrence in the poem.)We suspect it might also be important to him that the subject of the piece is taming – he seems to enjoy domesticating and dominating other people.