Stupidity: The gang is brutal enough to have Lavington killed; considering they know where he lives and that there's just a single housekeeper, it would have been miles easier for them to just kill or tie her up and ransack the house themselves with all the time they wanted, rather than involving the most famous detective with an obvious ruse and hope he'd find the object.
And All Through the House - S1-E2
Stupidity: The woman could've blamed her husband's death on the maniac, she didn't need to go outside to retrieve his body.