This bug(s) is extremely frustrating.
I test on my end and have no issues at all getting them to complete so trying to track down the issue is very difficult.
Here are some things to keep in mind: (according to the documentation I have)
1) You must be on the latest version of Dungeon Quest to accept the quests that are active. When the quests are made on the google side they use the live version of the game to verify completion status.
2) You must be connected to the internet at all times to complete these quests. This is a google requirement for Google Play Games.
3) You must have the latest version of Google Play Games Services installed on your device and you must be logged in.
4) The game must be installed from the Google Play Store. Google Play Games services will not work with a sideloaded application.