If the shapeshifter can duplicate Dean's clothes, why did it break in to Zach's house to steal clothes before the murder?
It didn't duplicate Dean's clothes. It stole his jacket after it kidnapped him - hence Dean walking around in only a t-shirt for after he and Sam escape from the sewer. Given that Dean's jacket is the most noticeable part of his wardrobe, the shapeshifter presumably just threw it on over whatever t-shirt and jeans it already had lying around, avoiding the need to completely strip Dean.
Further, look at the shapeshifter in the scene where they encounter it for the first time. What is it wearing? A grey t-shirt and jeans. What is Dean wearing under his jacket? Exactly the same thing. It only needed Dean's jacket to finish the look.
