The behaviour after 1.10 is indeed strange. I started a new play through (not NG+, clean 1.08 from the beginning) a few days ago and completed both Novigrad: closed city quests.
To avoid misunderstanding: closed city I: find the 3 keys and open a treasure; closed city II: help two bandits to...
Same here. Just started a new game a few days ago and was happy that this time I was able to finish the closed city II quest. Now after 1.10 it's marked as failed. I'm playing on PC.