At first, I just assumed it was a bug that characters who I know for sure have radiant quests weren't giving them to me. I had started playing with one character and got quests from the blacksmith and alchemist in Dawnstar, but then neither would give me quests on the next character. On my third character, I got quests from them, but not from the priest in Falkreath, who is the last one I need to help in order to become thane there. And the jarl of Falkreath wouldn't ask me for the Black-Briar mead on my person when I first met him – but he did later, after I finished some other radiant quests.

So, I'm hoping someone can confirm this suspicion for me: You can only have one or a few radiant quests of the same type (find a rare item, make a delivery for someone, etc.) at a time. I needed to find some random books for people before the Jarl of Falkreath would ask me for that mead. Does this mean I need to clear out some of my massive quest backlog just to get that quest from Runil and become thane?

Yes, you can only do a few of a certain radiant quest before you can do someone else's radiant quest. I was wondering why Ysolda wouldn't give me her quest but when I completed a few radiant quests on bringing back items, I got it.

Thanks for the reply. I cleared some out and managed to get the ones I wanted. Makes it a little harder to vie for thane-hood in multiple holds at once, but good to know the game isn't bugged so it's impossible. Wish that had been made clearer somewhere.