The quest log remains as it was when I logged in. It doesn't matter if I make any progress in a quest, complete it or even accept new ones, it remains the same.
The problem must be only in the quest log because I can complete quests by talking to the NPCs and doing whatever they ask me for.
Furthermore I can't leave any active quest from the quest log (it makes the sound but I don't really leave it).
Here is a pic where I logged in withe any quest accepted, then I accept a new one and the quest log information doesn't update. (My client is in spanish).