When Lily makes breakfast for Barney, after going out for groceries because there was nothing in the refrigerator, Barney makes it clear that he wants no food in the apartment. But in The Duel (2005), when Ted suggested Barney might move in with him, Marshall claims Barney cooks in the nude, which wouldn't be true if he allows no food in his apartment.
The armor in Barney's apartment is not actually a Stormtrooper's from the "Star Wars" Original Trilogy, but rather a Clone Trooper's from the Prequels.
When Brad and Marshall get back from the Alanis Morisette concert, Brad is wearing a concert t-shirt that says 2004 on the back of it, Ted said the year was 2006 at the start of season 2. But Brad very easily could have worn a shirt he purchased at a previous concert as many concert goers do.