When the agents are in Sammy's house, the piano is black. But in Sammy's flashback to his father being shot and putting his hand on the piano, the piano is light brown.
When the boy goes to the door, Reid goes after him and goes through the door. But then Rossi calls Hotch, Reid is seen going through the same door again.
When Sammy is drawing in the police station, in one shot, the drawing is of squares and triangles surrounding a detailed representation of the tread pattern on the bottom of Agent Rossi's boot in the center of the page, but in the next shot, the page is filled with just squares and triangles, with no boot tread.
During the opening scene, Sammy is wearing a white t-shirt under a light blue button-down. When Rossi & Reid meet Sammy, he is wearing a blue graphic tee under a darker blue plaid flannel shirt, presumably because the other clothes had blood on them. But while Hotch & Morgan are at the crime scene, there is a brief flashback showing Sammy at the piano wearing the two blue shirts. Additionally, when Rossi & Reid take Sammy & Aunt Lizzie back to the house, Sammy is now wearing a gray & white tee under a white/light blue striped button-down, which also matches his clothing on the music store's surveillance video.
Lafayette Parish, where this episode is set, is not on the Gulf of Mexico, and so would not be impacted by the oil spill. In fact, the parish contains less than 1 square mile of water area, it has no major lakes or rivers, despite the many scenes with and references to boats and fishing.
When referring to Sammy's parents, while discussing possible ransom demand, Rossi calls them Stanley's parents.