My least favourite quest is the shards/occulara simply because some of them were placed in such an annoying way and were frustratingly difficult to get to (with PC controls anyway) but chiefly because I hated the idea of looking through the damn things after I'd discovered how they had been made. Then having discovered this wretched quest was actually recorded in the Keep, I felt obliged to complete it at least once. I was totally underwhelmed by what I finally found behind the last door and it had zero impact on anything in the main game or subsequent DLC. If it had resulted in some artefact that was needed to defeat Corypheus it would have made more sense but it seemed everyone was meant to be hunting these shards for no perceived benefit beyond a bit of elemental buffing.
I also came to loath Bottles of Thedas because of the number of times they would cause the yellow circle to light up and someone comment how it was worth looking into, only to find yet another pointless bottle, again often after a frustratingly difficult climb to get to it or the need for the deft hands perk.
Of the main game quests, I disliked Hushed Whispers because I don't think time travel magic goes with the setting and so it seemed lore breaking to me, although it was enjoyable to play.
Wicked Eyes would have been better without the dependence on Halla statues, particularly since no indication was given as to how many you would use on a particular door until after they had been. It also seemed to have been set up for you to fail to acquire certain information because you might well not have enough statues until after going downstairs in the Royal Apartments but that involved passing a door where clearly something was going on; so why wouldn't you investigate there first? However, once you had done so, there was no going back. It was easy enough once you had done the quest the first time because you knew how it worked but first run it was a nightmare. I never found the locket because at that point I didn't have enough Halla statues and never thought to go back because I assumed it would just be random loot, like in the garden. Going into the Winter Palace our priority was meant to be identifying and eliminating an assassin but that turned out to be easy since they stand there and admit to it and so instead the focus was on us deciding who should rule Orlais, which made very little sense and was so arbitrary, dependent as it was on which doors you had opened. So great initial concept but rather disappointing in the delivery.
The final confrontation with Corypheus was also a bit disappointing. It didn't help that in all the preceding discussions with companions they seemed to be acting like it was a foregone conclusion, since they were planning on what they would be doing next/asking you what your plans were, when the boss guy was still out there. If you had done a complete play through before confronting him then you were just too powerful for him. Morrigan's speech when you first see the rift appear from Skyhold was just too overdone in trying to create a sense of jeopardy.
I liked Champions of the Just because it was a good way of introducing Cole and the idea of portraying the struggle with a demon trying to take over your mind. I also preferred this path because it led to seeing more of the Venatori and Calpurnia, who had a much more interesting story arc than Samson.
I also liked the whole sequence from closing the rift the first time, through the attack on Haven, until our arrival at Skyhold. That bit of the game worked best for me.
I also liked the Temple of Mythal, partly because it gave me the elven lore I was longing for, but also for the puzzles and the Well of Sorrows, plus the spirit rising up at the end to confront Corypheus. It definitely put some of the magic and mystery back into the story.