Production-wise, the artwork is beautiful. The animation may be static in most places, but the camera work and the tone of the story makes up for it. The OST suits the mood, though unremarkable.
For a story about a poet being a detective, it doesn't feel like a detective story. There's rarely a battle of wits or the tension that occurs when solving a mystery. That being said, I think the anime itself is more interested to how we as the audience solve the mystery. The characters' dialogue and routines, the way the camera shoots the scenes would often become clues for the viewers to think about. They can even be a form of foreshadowing, which definitely shows in the final episode where the key to a certain mystery is just thinking about what's already established before.
Furthermore, Woodpecker seems to be about the relationships between the characters, particularly the two main leads.
Of course, the show's pacing and writing aren't necessarily amazing. It can feel slow at times or uninteresting, but it's still an okay watch. The characters themselves are fine. While the two leads seem to be the most fleshed out, most of the others seem flat in comparison which doesn't have to be bad since those flat characters have okay personalities and they don't have a character arc so it makes sense.
Overall, Woodpecker Detective's Office may not have the best experience, but I'm still recommending it because it's an okay experience.
