Sherlock is a fox and Moriarty is a wolf to give them distinction from the canine cast in the series.
The show was a big hit in the United Kingdom, the home of Sir Arthur Conan Doyle and his creation Sherlock Holmes.
Professor Moriarty is dressed in a suit, monocle and cape. This was the classic attire of the gentleman thief Arsene Lupin. Hayao Miyazaki had previously worked on adaptations of "Lupin III", which featured the adventures of Lupin's grandson Arsene Lupin III, as did Kyôsuke Mikuriya. Additionally, Inspector Lestrade is designed to resemble Inspector Zenigata, Lupin III's nemesis.
Hayao Miyazaki directed six of the episodes, then production was halted due to legal wrangles with the estate of Sir Arthur Conan Doyle (the creator of Sherlock Holmes). By the time these issues were settled, Miyazaki had moved on to other projects, so the rest of the episodes were directed by Kyôsuke Mikuriya.
Hayao Miyazaki wanted to present Mrs. Hudson be the real genius, smarter than both Holmes and Moriarty. This change in characterization was overruled by the studio.