I always love threads like this on other forums as a way to see what ideas other people are toying with as well as broaden your idea of what would make a great DH adventure. As is customary I will start us off:
Time Trial
One of the Inquisitor's trusted servants has gotten himself in hot water on an imperial world. The acolytes are tasked with proving his innocence in the matter. A local servant girl has accused the man of violently assaulting her after she spurned his advances. Appalled at the attempted destruction of his property, the girl's employer has pulled strings to ensure the trial falls during the Festival of the Emperor's Ascension (IHB pg. 197) when it is believed that no false judgement may be passed. This world in particular takes that particular belief very seriously.
The players have a mere 72 hours to prove their comrade is innocent, during which time they will likely run afoul of something much more sinister. It turns out the accused was undercover investigating a Cult of Slaanesh when he was arrested and charged with the crime. To make matters even more intriguing, one night the prisoner is visited by a mysterious hooded figure. Upon further investigation the players may discover that this mystery figure is in fact the very girl who has laid such accusations at the feet of their ally.