Right now the conflicts that I run into when dealing with player complaints is overlapping dialog with the same NPC. Example: You've got two quests open (or more) which require you to talk to the same NPC. One quest will take precedence over the other depending on the situation, and you will not be able to progress in the lower precedence quest until you finish the conflict with the higher ranked quest. As we update the older quests with some new features and abilities these kinds of conflicts should reduce drastically. I hazard to say it will never happen again, but the improvement will be significant.
Now, to address the issue in Prolix's example. There is no situation that I can think of at this time where any active quests, completing them, would keep you from finishing another quest that you have open. Now, completing one may keep you from getting a quest that you have not yet started.