In the first appearance of Donnies sandwich he had taken a bite out of the center. In the following shot the bite is from the corner.
During the proceedings, Maris tries to go after Niles for alienation of affections, however alienation of affections is only recognized in a few states, none of them being Washington where the series takes place.
Martin tries to persuade Frasier that he has to lie to do the right thing for Niles during the deposition by telling a story about a time when he lied in court about reading a suspect their Miranda rights in full, otherwise the suspect would walk free. Miranda rights are not read to suspects when they are being arrested; it happens when they are about to be questioned afterwards. And even if he hadn't been read his rights, it wouldn't mean he automatically goes free. It simply means anything he said under questioning would not be admissible against him in court.
At the coffee shop, Frasier pulls open Niles' briefcase and sees that Niles has a baloney sandwich in it for lunch later. Niles would never put something that needs refrigeration in a briefcase where it would go bad. He would know better to put it into an insulated lunch box. He would never eat a rotten meat.