okay. varric's Friendly Concern quest
according to Mary Kirby in this bioware forums thread, Friendly Concern is supposed to trigger after sleeping with at least one character and completing at least one qunari quest. according to the replies to the thread, the quest only triggers for Anders romances with very few exceptions for other characters
supposedly, this was fixed in patch 1.03. according to the wiki talk page, however, while the quest might trigger for all romances now, there's a possibility that it won't trigger until after all that remains, regardless of any other quests completed beforehand.
also, according to Mary Kirby in the above forum thread, it's deliberate that hawke is still supposed to be able to complete the quest even with a relationship that has been broken off, with special dialogue options for such a case.
so looking at the game files, the way the conversation actually works is that, if the quest has triggered for you, when you go talk to varric the game checks TWICE to see which character he's talking to you about. first it checks the standard "active romance" flags, but if none of those are true, it also checks special flags that were set specifically for the quest that also indicate a romanced character. I believe these are supposed to facilitate the special "breakup" conversation with varric, if you haven't initiated a new romance after the breakup. however, according to the wiki, this is only possible with anders after cutting off the relationship in Night Terrors, and the conversation ends early rather than playing out as intended.
so there are two different ways that this quest is initiated, both of which set flags to initiate the quest as well as the special "character romanced" flags I noted above
the first is flag 22 in act00pt_main. this flag is set within the following plots: Blackpowder Courtesy, Offered and Lost, Following the Qun; Prime Suspect, All That Remains; and Night Terrors. however, this flag, rather than checking all four "romance active" flags, ONLY checks anders' flag four times. this is why this quest only triggered for anders prior to the patch, and still might not trigger until after All That Remains. this wasn't fixed in the patch.
the second is in the area script for the estate. this checks different flags than the standard "romance active" flags, flags which would indicate the romance had been intimate, but it DOES check them for all four characters, and it does this at the same time it sets up the cutscene for Hawke's partner to comfort them after All That Remains, so a romance would have to be active regardless. this must have been the part they patched to work.
so there IS a problem here that the quest only triggers for relationships that are active at the exact time it initiates the quest, and only sets those flags at that point, so there's no way to get the "broken off" relationship dialogue with varric having, for example, refused the relationship at the end of the romance scene itself. see: the exception of anders in Night Terrors, which still doesn't work for reasons it's currently too 1 am for me to care about.