At 17:50 after House says "You have pretty hair" to Cameron, the fingers on his left hand change positions between shots.
When Adam begins choking he moves both hands to his upper chest. When we see through Adams eyes again his hand is still on the blue glass. In the next shot his hands are still on his chest.
Adam supposedly draws lines on the chalkboard to express what he sees. But several times we see can through his POV and until the end there are never "lines".
The side plot involves House being seduced by a 17 year old stalker. Repeatedly through the episode it is mentioned that she is under aged. However, the age of consent in New Jersey is 16. The character herself indicates that the age of consent in Iceland is 14 to try and convince House that it would be OK to have sex with her, it's odd that she would know the age of consent in Iceland but not the state she lives in.
The team finds calcium carbonate in Brandon's stool. House determines that the child has been eating blackboard chalk. However, despite its name, blackboard chalk is actually made of calcium sulfate (gypsum), not calcium carbonate.
Calcium carbonate is occasionally used as an anti-diarrhoeal (as indicated by House while discussing the case with Foreman in Cuddy's office). However, he later defends its use in Adam by reasoning that he had constipation.
There is no blood stain seen from the underside of the carpet. At the end when the old carpet is being installed, the blood stain is not visible until the carpet is fully unrolled. Large blood stains would have penetrated the full layer of carpet into the old padding. It should be visible on the bottom before as it's being unrolled.
When house walks into Cuddys office to demand his carpet back he walks on his right leg without use of his cane.