I am at the final stage of the quest Forbidden Legend: Reforge the Gauldur Amulet, and I have just defeated the 3 ghosts but nothing happens? I have seen some videos showing some father figure is suppose to appear, but nothing happens. I have done the quest twice now but with the same result.

Reload before you enter the cave.

One thing you haven't mentioned is whether you have actually moved to the end of the chamber to use the mechanism that will reforge the amulet. The ghost does not appear until you do so and the amulet will not be reforged. Just defeating the brothers does not initiate the action, you have to be in a certain spot and attempting to reforge it.

One the second run I reloaded inside the cave but went outside for a few seconds and then back inside. I will try to return to the cave now and redo the thing.

Yes I went to the alter and waited and jumped around.

Roger that, just checking. Sometimes little things can be overlooked and will have a profound effect. Bugs can be common but there is usually a work around. Let us know if you get this one fixed so we can give you a "That a boy!"

Just tried once more but with the same result. Strange thing is that once I defeat the 3 ghosts, there is still a red enemy-dot on the radar showing. But the room is empty and I am out of combat. I guess that mission is just bugged. A shame and I would have expected that these types of bugs would be fixed by now. Oh well.

That never happened to me fortunately, my only bugged quest was "Blood on The Ice" which is bugged for everyone. Since it is not working for you at the moment hope is not yet lost. I managed to even get around that bug on 360 so there is hope. I would suggest going and doing something else for a while, maybe a couple of weeks or even a month game time and returning then try again. The bug may work itself out in the meantime... or it may be forever broken. There is no way to know for sure but don't give up yet! Something may fall into place in the program later that will allow you to finish the quest.

Are the three ghosts up on the raised area? If so, best suggestion I can make is to re-start that dungeon.