A few simple suggestions for the Challenges section:

Daily: not a problem.
Missions, Achievements: group the achievements in some different options. For example, in addition to the existing by-nearest completion, add an option for by-dungeon and one by-character. Also, display the completed items (default view would have these grouped at the bottom.
Event: similar to the Missions and Achievements, have the nearest completed at the top.

Missions, Achievemnets and Events: in addition to expanding the group options, have the group collapsible. For example, finding the Monthly event dungeon becomes difficult part-way through the month because of the amount of other events on top. Being able to collapse a group means simply not seeing the items int he group but instead only a header for the set: in the Event tab currently "Clan challeneges", "Dungeon challenges", "Monthly challenges" (or by name of the event 'cause I never remember those).