A note: with its strong foundation in dealing with knowledge, archives etc., the Ark will have a very strong handle on noblemen. Why?
*You need to legitimate your claim to a title. Of course there are documents to prove your right. Kept by an Archivist. Of the Ark.
*You need novel weaponry to defeat your foe. It was invented recently. By a scholar of the Ark.
*You need religious support to motivate your troops. Priests of the Ark can do that. (just look at the Investiture Controversy in the 11th-12th century for a conflict between priesthood and nobility).
*You need competent magistrates to run your realm properly. Of course they are members of the Ark.
Simply denying services will calm many an uppity noble quite swiftly. If the Ark withdraws its members from a realm, it will soon become a hillbilly backwater - especially considering that intellectuals will drain from there to realms where the Ark maintains presence.
I can see them involved in a grand, if silly quest: "Magic is suddenly failing! We are doomed!" Of course, it's just Bobeerin overpopulation.
A tyrannical regime could use them out to sniff out wizards. And once they taste a spellbook, wizards beware!
Adorable. Alas: what is their origin? How does their intelligence manfest? How do they interact with cultures? Any predators or enemies? Etc.
Well, this raises the classic Paladin issues: does being evil but not actually doing evil make you a target for prosecution?
How long does it take for a crime to 'fade' and no longer be detectable by the spectacles? What has to be done to wipe a sin from you?
Also, what is a grave sin to one is an amusing antic to another - for example, gay sex or blasphemy. If they detect solely crime, which law system do they use?
What about making the depictions of the spectacles dependent on the general perceptions of the wearer? So a very lenient person will not see minor sinners as demons, just as humans, while an intolerant one would find himself surrounded by the vilest fiends.
This is so unique and hillarious that the short description provided is truly sufficient.
I'd add but two things:
*Traceability of the coin: can mediums or the like trace where a coin has been?
*Interception of the coin: I echo a previous comment: could a thieving Potter clone snatch them from mid-air to enrich himself? Sure, their enchantment needs to be temporarily suppressed, but perhaps... perhaps catching them is something only a few extremely dextrous individuals could do, making Falcon Coin theft a way of living for a few, while ensuing most transfers are safe.
This is "so DnD" - the lore is decently written, but the whole "weapon made to stop the greatest foe" approach has been used too often and is made only slightly better by having been made by two working in unison.
Also, it's a sword. With a dragon inside. That turns you into a dragon. I know Dungeons and Dragons is supposed to be about as much about dragons as it is about dungeons, but overdoing it with the dragons may lead to diluting their dragony awesomeness and making them less special (been there, done it).
This said, the sword can be a good McGuffin; I'd have included a limiting clause though or some sort of drawback which makes players less inclined to keep it after they down the Big Nasty.
Another note: the bargain Lord Brax struck with the dragon could have actually borne the seeds of his demise - you write he had the power to claim the soul of the dragon - so the dragon in turn should possess the "power, strength, endurance, and knowledge" to defeat him, in turn. Hence, the dragon-turned-blade could indeed be fed a stream of thought betraying the villain's plans or next strike in that battle (knowledge), drain him of vigor feeding its weilder and striking true as defensive enchantments woven by Lord Brax fail miserably to deflect this one weapon.
Also, welcome to the citadel.
You could go with a spring mechanism, with a winch to draw back a hideously strong metal coil... or you could make it a Gauss crossbow, propelling the bolt along the barrel with whatever technobabble strieks your fancy.
Also, I don't think fletching per se has to impart a spin on the arrow, it ensures that the arrow does not tumble.
As it is, the technological solution does not make too much sense.
On a different note - you can really go way out there: what if the bolts are magnetic - and coincidentally, the magic used to enhance the armors of the cavalry improves all the properties of the metal, including attracting magnets, disproportionately so?