How can I measure the "health" of Bitcoin? What are the metrics that matter when evaluating the overall "health" of Bitcoin? 

What are the thresholds?

Specifically


Economic (e.g. velocity, days destroyed, market volume &amp; beta)
Technical (e.g. rate of difficulty change, block size, tx fees, size of the chain)
Diversity of stakeholders (who are the market movers, large investors, what are their intents: profit vs stability)
etc.


Specifically, I'm trying to get an understanding of financial health of a system that proclaims to be superior to the one it's trying to replace (or compliment).
This strongly depends on what you think makes a financial system healthy.

As long as there is no challenge to the core of Bitcoin, distributed no third party controlled transactions, there is no need to worry about any of the technical aspects. Stakeholders are the major problem here, the hashrate distribution being the clearest example. Stakeholder power must be distributed to preserve the nature of Bitcoin. Hashrate has a hard limit at 50%, but even close will cause less reliability. Other stakeholder measurements have no clear/hard limits.

The health measure then comes purely from the hashrate (indicating security and current interest in the minable Bitcoin) and the amount of users connected to the network. Sadly the users connected cannot be measured correctly due to Bitcoin wallet services.

Any other metrics can show you what happens to Bitcoins, but not everywhere else. Some indications can be given about how Bitcoin are used, but not about their actual "health". At least not in any measure of health I can currently see to be valuable. I'd consider transaction origin and destination diversity to give some indication of user diversity, which would indicate how much Bitcoin is used, which would indicate robustness through diversity.

FYI: Many interesting graphs are here. They say something, but do not clearly indicate health. I do think most of them have "better" or "worse" directions, but they are fairly easily manipulated, especially in unhealthy circumstances.