Frost speculates that the husband rushed to the wife's office to take over her senate seat, but spouses of elected officials do not inherit the political office like some heir to an estate. Depending on the office and district, replacements are either elected in special elections or appointed by a higher up elected official.
Maura states that 53% of women are the main household breadwinners. Frost moans and asks why he doesn't have one in his household. Frost is a bachelor who lives alone.
On several earlier episodes Maura is the fit, avid jogger who must drag along the woefully out-of-shape Jane, but in this episode the writers depict the opposite.
Jane says she found blueberries found in vomit at the scene of the shooting, but the location of the shooter had not been determined at that point so she could not have possibly found anything, including vomit.