My Monarch is definitely NOT married! In fact, NONE of my hero sims are married, yet when I try to play the quest for an heir which requires the monarch be unmarried, all of the approaches are grayed out and I'm unable to play the quest. Now the monarch does have several Romantic Interests, and also a child by one of them. Does the game then "think" he's married because of these relationships? Do I have to end the relationships to play this quest? Or is the quest invalid because I already have an heir? I suspect the latter may be true. Can anyone confirm my suspicion?

monarch doesnt have to have any relationships, the monarch will end up having to work for relationships in the quests and choose a suiter. one of the steps is selecting 3 suitors. you can have a child already from another relationship, i had a game where my monarch had a child with the bard out of wed lock.

What does it say when you hover over the greyed out options?

simbalena, it says nothing when I hover over the approaches. The buttons are actually translucent, not grayed out, sorry for the inaccurate description (I tried to take a screen shot to show the quest book, but it didn't work!). This is the "A Political Marriage" quest. I can click on the approaches, but the arrow to select the approach and move on to the next page of the quest book to select the heros is inactive and won't let me select and move on.

For that one quest I think you need to have Effenmont as a scouted territory (and allied) - it's different from the Heir to the Throne quest.

If you used showallquests, the "Political Marriage" quest may show up before you normally would be able to see it (It appears when you scout out Effenmont, as mentioned.)
I think at least one of the approaches also requires a spy.

and you can't be courting anyone else .. thats what got me on this quest I forgot I was courting an N
PC then had to track her down and break up before I could go forward.

Ah! That's probably my problem! I did the same thing when playing the Golem quest. Forgot to form an alliance with Ticktop! Guess I should just form alliances with all possible countries to preclude future problems! Thanks to all for your responses!

Edit: Where do I find Effenmont? It doesn't appear on the tactical map. Must I complete some other quest in order for it to show up on the map? I recall seeing a map to Effenmont in the Village Shop. Must I buy it before I can play the quest?

Yup you have to buy the map and discover Effenmont -using the boat- with any of your heroes (you can also get the map for free during a random event while going to the village shoppe)
It's also true for Gastrobury.

Dang! EA must think we're all psychics! Thanks for the info, happyopi!