After Barkin and Rufus are uncombined, Rufus is wearing a miniature version of Barkin's clothes from before their combining, and Barkin is naked. Barkin borrows one of DNAmy's frilly robes, and everyone escapes her lair. After Dr. Possible rescues them from an avalanche, they race down to the lodge and crash. As they initially sit up, Barkin is wearing his clothes, not the robe. (When the scene cuts back to them, he's once again wearing DNAmy's robe.)
Throughout the episode, Mr. Barkin's hair is dark brown. But when he unmasks DNAmy's pig-henchman, his hair is light brown.