As indicated above there are some areas of this topic that are already covered by technology. However, if we did want to be audacious then the following would be a worthy challenge that would benefit health (by detecting anomalies that indicate potential health problems, and by checking nutrient levels in the body).
This challenge would avoid the need to extract blood samples (needles in particular*) and would result in a device that is simply placed on the skin (e.g. like a fitbit). It would identify specific molecules within the body, estimate their concentration, and derive probable conclusions [perhaps with AI assistance].
One way, but not the only way, to do this might be to shine infrared light into the skin and note the spectrum of the reflected signal. Infrared spectroscopy already provides a useful way of identifying molecules in other applications (e.g. http://bit.ly/brainHealthBlog - select the Spectrum filter tag).
(* An alternative to needles is to adopt the ultra-fine needle like features on nettles. This could deliver medical drugs or take samples. An innovation elsewhere has adopted a similar approach.)