This is a nice end for this group of episodes (apparently called a "series" in the UK and a "season" in the US). What's best about it is that it has all of the recent Father Brown "regulars" as a sort of re-union episode. Also it has attractive vintage cars and impressive estates, which has always been part of the appeal of the show.
The only thing wrong with this episode is that there is too much going on, too many characters and sub-plots for a 42-44 minute drama. As such, it's hard to get a grasp of what's going on, and virtually impossible for the viewer to predict the outcome. They tell you what happened, but that's not as interesting as leaving clues to let the viewer have a guess.
If they'd had a full hour to flesh out the ideas in this episode, it likely would have worked a lot better. There should have been more regarding the young "Lord somebody" (the guy with the long hair) and his possible motivation as a suspect, as well as more development regarding the big-shot potential PM and the people around him (such as Ruth, the doctor, and the big-shot's wife). They also might have developed a bit more between Flambeau and Lady what's-her-name. Maybe also more between the inspector and Goodfellow.
As it stands, there's a lot of confusion in the episode. I realize they had less than 45 minutes to fit in a complicated set of plots and sub-plots, so I'm only docking it two stars for that. Possibly they could have made it a 2-part episode, but I don't think they've ever done that with Father Brown.