As it stands the two quest sections, the main "Quests" guy and the "You have a new quest" guy, both block players from interacting with a portion of their home screens. The 'Quests' button interferes with access to the Laboratory (and therefore research) while the 'new quest' messenger interferes with scrolling on chat.
"Quests" could be moved to a smaller button (no floating head associated) underneath the Co-op/PVP queue, and a notification (flashing like chat button ie) could show when a new quest had been given.