Elder Scrolls 4: Oblivion handles the quest tracking concept you speak of quite efficiently Dajoji, not sure if you have ever played around in that game though.
It essentially has a list of all quests the character is currently on, with the last entry info listed under the quest title to give a brief over view of where the character left off on that particular quest. The player also has the ability to click on that overview, which then brings up the entire quest history from the beginning to that point in the quest so they can go back and re-read the entirety of what they have done so far in the quest.
To do something like that efficiently in PS though, would take a little overhaul of how character quests are stored in the DB. That being, a way to have all quest dialog for all possible quests for each character must be developed, but then simply have each bit of dialog for each quest have a show/hide flag per each character, and when the character does the required activity that displays the next dialog in the quest chain, that flag also gets updated from hide to show. Then, its a simple query on the db for show all dialog for (insert main quest title here) where (dialog flag name = show for when the player wants to pull up the chat history about that quest they are on.
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My thoughts on this subject was that a separate window could be created that would simply pull up the last 50-100 lines of conversation that character has had since last login. That way the player can get a refresher of what happened last time they logged in, and if they really need to know more, they can always refer to their saved log file.