In some ways, The Crime at Black Dudley is a very typical British country house mystery. A bunch of upper class people are invited to a party weekend at some god-forsaken, off-the-beaten-path estate. They arrive to find they don't necessarily know each other, and are a bit curious as to why they have been chosen. The house comes complete with creepy relative, hostile manservant, and a very weird family tradition. When a murder occurs, it's only the beginning of what will turn out to be a simply disastrous weekend. The women weep, the men engage in fisticuffs, there are secret passages, hidden identities, and a few fiendish plots.
The main character is Dr. George Abbershaw, a mild-mannered physician who occasionally consults for Scotland Yard. The actual detective of the piece is Albert Campion, who both extremely intelligent AND extremely weird. Although Dr. Abbershaw in some ways functions as a Dr. Watson, he is less privy to Campion's actions and motivations. It's a bit like seeing a Sherlock Holmes story from Lestrade's point of view--glimpses of the great detective at work, hints of his motives, some short and somewhat confusing explanations, but never a full picture of what is going on.
The characters were pretty well drawn and interesting. Although Campion was used sparingly, I can see why Allingham decided to make him the star of her series rather than Dr. Abbershaw. The plot was all right, though nothing particularly surprising or thought-provoking. On the whole, it's a decent murder-mystery, but nothing special.