When no longer wearing his trademark suits, Barney wears a shirt depicting the cover of the book "Die Neue Wohnung" by famous architect Bruno Taut, indicating that the shirt might actually belong to Ted. Barney probably took all his "new" non-suit clothes from Ted's more casual wardrobe.
The music accompanying Barney's hidden suit in the restroom in MacLaren's pub is "Bullwinkle pt. II." A reference to a scene in Pulp Fiction (1994). Where, to the same song, Vincent Vega (John Travolta) shoots up heroin.
Marshall actually slaps Barney when Barney's rubbing his face on Marshall's suit, but they don't keep track of this one. If they did this would be the last of the 5 slaps Marshall could give until the later shown "Duck Tie Saga".