This thread "GQ will not complete" and the thread: Daily and guild quests not completing are the same, and both are a bit of a jumble of issues.
Above threads merged.
The core problems appear to be less that Dailies and GQs aren't completing but that certain Trade Quests and Buff Quests are bugged.
The workaround for the Trade problem, also affecting: "The Trade" Level 12 Tutorial Trade Quest seems fairly consistently to be "Have someone else make the offer."
Trade ~ Quests to Buy/Sell [x] Resources Not Registering
Workaround:

Originally Posted by
Xibor
Today, one daily quest and one guild quest. In both cases it took two players to both do their end. Explanation:
I sent a player 5 wheels in return for some fish, then sent a trade asking for wheels and giving fish. Result: Their quest completed, mine didn't.
Then that same player did the same thing from their end, and mine completed.
This was repeated for a different quest with a different player. When they made the offer, mine completed but theirs didn't. When I made the offer, theirs completed.

Originally Posted by
Kit_
trade x amount of resource, using direct trade and trade office, any trades set up by the quest owner do not register for this quest. work around this can be done by getting a friend or guildy to set up the trades for you and send them directly - so if you need to buy 10 fish, your friend sends you the 10 fish and vice versa..
There doesn't seem be a workaround for Buff Quests not registering.
Buffs ~ Quests to Buff Friends Not Registering
Workaround: Currently no known workaround.
And as mentioned above, this: Can no longer cancel the Guild Quest is a separate issue.