An additional commandment I can think of is that the crime has to be something significant, like a murder. I wouldn’t want to read a story about a detective solving a petty crime or finding a lost dog.
"You're talking about your dog? I don't do dogs." I said.
At this point, the husband slid an envelope across the desk filled with cash. It was at least twice my daily rate.
"Look," he said, "I need this done, and I need it done discreetly. Find the dog, or bring me its collar." The woman began to object, but a glare from her husband stopped her.
This was more than a missing dog case. It had to be, no one put up that much, in cash, up front just for a dog. You put up posters in the neighborhood, you don't hire a PI. Alarm bells were ringing in my head, but the rent was due, and Aberlour isn't cheap.
I opened my desk drawer and casually slid the envelope into it. "Do you have a picture of..."
"Beaumont. His name is Beaumont," the woman supplied.
...
Dirk Gently[0] would like a word...
[0]] https://en.wikipedia.org/wiki/Dirk_Gently_(pilot_episode)
A violation of Knox Rule number II.
A reasonable point. Although I'd say that humor (if done well) is a boon, rather than a detriment to mysteries (most fiction, actually).
And cats always make things better[2]!
As someone who enjoys mystery novels, I've noted that minor mysteries are often used as a device to bring the detective into situations where larger issues may be afoot[0][1].
It seems to me that if a mystery is engaging, the underlying "crime" isn't as relevant as the storytelling, clue planting and the thought process of the detective.
At the same time, mysteries generally deal with serious crimes (especially murder), as it amps up the (fictional) stakes and provides a reason for the interest and participation of the detective.
But that needn't be the case -- as long as the mystery is interesting, the prose is of good quality and the characters engaging. At least that's my take.
[0] https://en.wikipedia.org/wiki/The_Red-Headed_League
[1] https://en.wikipedia.org/wiki/The_Adventure_of_the_Clapham_C...
[2] cf. Lillian Jackson Braun's "The Cat Who..." mysteries[3].
[3] https://en.wikipedia.org/wiki/Cat_Who_series
Edit: Fixed reference indices.