You know those names for groups of animals that span the common ("a swarm of bees," "a pack of wolves") to the obscure ("a sedge of bitterns")? Well, if you're in the mood for mind-bending, here is a page dedicated to bird-groups. I never called goldfinches plural anything but a flock, but having seen the tiny things at their tiny meals of, I would agree, a "charm" is somewhat more descriptive.
What brought on this particular subject was the rediscovery of a note I wrote myself last year, about a "Pfretzchner." I believe this was a German-made viola that I had some slight acquaintance with, but it was the spelling that impressed me most. It would make a grand collective noun for use in linguistics: "a Pfretzchner of consonants".