At 18:14, Ducky hangs his coat up ,and hangs his hat just above it. The subsequent shot from the other angle, at 18.24, show the coat on the other side of the coat stand, although the hat hasn't moved.
(At 00:14) Gibbs, Pride and Fornell sit down to eat "red beans and rice" that Pride has prepared. While the dish is in fact red beans over rice it is not "red beans and rice" as you would have in New Orleans. Something that Pride, being from New Orleans, would obviously know. In New Orleans, the dish known as "red beans and rice" is red beans cooked together with rice and spice slowly throughout the day. Therefore the rice is colored red by the beans and it is a simple, basic (but delicious!) dish that is often served on Mondays in the tradition of Monday being "laundry day" thus allowing the red beans and rice to cook slowly all day while the laundry is being done. Thus the comment from Fornell "It must be Monday".
The NCIS New Orleans resident agency is located on the grounds of Joint Reserve Base New Orleans in Belle Chase, not within New Orleans city limits proper.