I could not get started with Falkreath's Thane quests until I started clearing up misc. quests. I needed to turn in the mammoth tusk to ysolda to get the Briars-mead quest. I then spent over 3 hours doing other misc. quest until I got the "kill bandits" quests.
As has been stated, there are radiant quests that will block the Falkreath Jarl from giving you quests until you wrap them up.
Skyrim should have had a work around for this when they released the DLC, seeing how common this problem is, IMO. Or made this DLC without achievements.