This is kinda odd to me: while the ULC isn't exactly a banner of training for their clergy, one would think that the First Amendment would trump a lot of the stuff out there.
But, so far, it appears that at least New York City and North Carolina don't accept ULC ministers as legal marriages.
Curiously, the ULC purports to be legal in all states. Gotta love it. I guess they're technically correct: the First Amendment would make them "legal" in all states, but individual states occasionally haven't had a challenge that would test case law that ruled against them (as in the case of North Carolina), or else the courts have ruled against the ULC. (Wikipedia has a list of court cases involving the ULC, most of which are favourable to the ULC.)
tesinth has also informed me that his ULC ordination isn't valid for marriages here in Ohio, but I'm not finding info on that yet. Then again, he's the one with the certificate, so he'd know better than I.
Because I'm registered with the state under my ADF credentials, I don't have much to worry about here. On the other hand, depending on laws, I might need a physical meeting place for the Grove to legally marry people in certain states (like the state of New York, though because I "have" a congregation, I should be okay on that).
ADF's "Law and the Church" course gave me a solid footing on how to slip through and search out a lot of this information, and I'm happy to have that. Just the act of finding as many laws as possible really gave me a leg up on the process. I know who to call to resolve questions that the statutes don't seem to answer, and I know how to dig through case law in some cases as well (though this particular skill is not as good as I'd prefer, I admit).