I lunched with a fellow writer yesterday and we discussed that topic, which is about as useful as "How many angels can dance on the head of a pin?" The answer has to come from the story itself, and the author has to make intelligent decisions as things progress.
Another friend in the business made the point recently that mystery is a little different from other genres, since "extra" characters are needed to create red herrings and give the reader alternate guesses. So the question becomes "How much time should an author spend on those extra characters?"
Some authors are good at sketching a realistic portrait in a few sentences then bringing that character into the story just enough times to make him a viable suspect or an interesting sidelight to the main story. Others get bogged down in creating backstory for every single character, which slows the pace and becomes irksome to the reader. I've found myself muttering something like, "I don't care how funny you can make this woman, just get on with the plot."
Like so many things in writing, choosing the number of characters you will include and how much you will tell the reader about them is a balancing act. For me, concentrating on the main characters is crucial, especially at the outset, and keeping tertiary characters intriguing but brief throughout is a good idea. Maybe the next book can expand on the secretary's humorous personal secrets.