If you call someone assiduous, it's a compliment. It means they're careful, methodical and very persistent. Good detectives are classically assiduous types.
Assiduous comes from two Latin words: assiduus, meaning "busy incessant, continual or constant," and assidere, meaning "to sit down to" something. (Funnily enough, we also get the word sedentary, meaning someone who doesn't move around much, a lazy couch potato, from this same last word.) Although we tend to think of sedentary types as being the very opposite of assiduous ones, many assiduous activities (like writing, thinking, or detective work) are best done sitting in a chair.