It should be possible to nest host groups.
There should be a hierarchical display for viewing such groups in most places.
All group dropdown selectors should show groups hierarchically whenever possible (a lot of subgroups could expand them a lot).
Circular nesting should be checked and prohibited.
Must perform well with large amount of groups and hosts in them in all locations in frontend and in server, where relevant.

open questions :

Should groups be able to contain both groups and hosts ?
Should group be able to be a member of several parent groups ?
What about upgrades - maybe it's worth providing simple upgrade path for people who use some notation schema currently (for example, allowing definition of group separator, thus group "UPS :: Something" group would create two groups - "UPS" and "Something", where "Something" would be a subgroup of "UPS").

open questions, large areas :

Permissions (general, global scripts, maintenance, actions...)
Action conditions
Action targets (groups)
Maintenance
Dropdown entry "all"
Filtering (almost everywhere - should it include subgroup elements etc...)
Search result displaying (for host groups)
Displaying in network maps (to include subgroup triggers or not, what about host group element displaying...)

forum threads :

http://www.zabbix.com/forum/showthread.php?t=11425
http://www.zabbix.com/forum/showthread.php?t=17559