Some you'll have to get the normal mode quest and do some dialog before you can drop it and pick up the hardmode version (e.g. Boarding Party/Foundry). You don't have to actually run them on normal first. You might have to redo the dialog every time until you do though.
not sure if that's entirely accurate.
when we did boarding party the other day, none of the 4 of us had ever done boarding party on regular mode. there's an additional NPC right outside the actual flashpoint that will simply give you a quest for hard mode. in fact, you cannot pick it up if you have the regular mode quest.