It's happened to me too. The last one was the Staff of the Furnace. I killed the monster, got the Staff, and when I return to the quest-giver a window pops up saying, "Locate the Staff of the Furnace".

Those two quest didn't complete either for me

I'm also having troubles with completing the quest: "Diseased Livestock"

Kill the slaver does this for me.  In addition, I chose to hire the giant the first time, and then the slaver fight event was given to me again when I returned the girl to the farm. The second time I killed him.

I have encountered this to. Also they need to work on giving more information about quest. Where is the quest log?  The little quest icons on the left side of screen do nothing when clicking on them (They should pull up the log and show where to go for the quest.

Besides the slaver quest (killed the slaver but could not bring back the kid) I had trouble with Mantle of Stars quest: When the crystals were requested I had them already so I did not need to kill monsters for them. Both the request dialoge and the point to the dragon dialoge happend directly one after another, but I could never find the dragon.

In the quest where you get Haitan, is this type really supposed to be a useless figure? I can't give him powers like the champions so I have a unit with a fire skill and no attack/defense.