When Ellen Rogers enters the room to see her daughter we can see the kidney dish on the table in front of Callie changing positions. It is in a different position when she says 'you haven't been that for two years' and when she starts coughing up blood. The first time it is on the lower left corner of the table in a diagonal position while later it is in the lower middle of the table perfectly horizontal.
The Confederate general reenactor was in fact wearing the rank insignia of a Major, which is a one star. All confederate generals of every grade wore three stars in a wreath. Furthermore, it was a six-pointed star, whereas confederate rank insignia used five-pointed stars.
While skeet shooting, House complains that the "sights are off" on the shotgun. While shotguns used for skeet (and trap) do often have a bead at the end of the barrel, they do not have sights - the shooter "leads" the target, with both eyes open to get a "sight picture".
However, House is only using a cheap (and incorrect) excuse for his obvious ineptitude at skeet shooting.