My title says it all. Two of my pet plot peeves are stupidity (the characters do something stupid to move the plot forward) and contrivance (circumstances beyond credibility to move the plot forward). So masterful in so many ways, it is a shame that this plot seems written by a drunk amateur shouting out random ideas ("hey, and then this could happen!...").
The best bit was Stanley Tucci's and Atkin Estimond's neo-Sherlock/Watson rendition. Great character concept, actor pairing, and portrayal. The only downside (again) was the fairly contrived scenarios they were challenged to solve. But I could watch them banter all day.
I would reboot the series around Tucci and Estimond and hire a professional writer to focus on plot structure and you would have winner to rival "Sherlock" and "Elementary".