Sorry, I think some of these features were mentioned somewhere in the forum, but I have strong tendency to summarize...
Only important features list.
Group search:
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better phrase search - search should look for the phrase anywhere in the group name, not only in the begining (implicit "wildcard like search: *My phrase*"
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pagination in the list of groups is not working properly (now it allows me to browse only up to 40th page of groups, although there are more! This makes some groups inaccessible.
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pagination in the list of groups should be improved (at least like in user gallery - direct jump to the end of the list shall be supported + feedback how many pages of groups are there). Predefined jumps to selected letters in the groups list ordered by name, to dates in groups ordered by date of creation will be nice too.
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more sorting/filtering options for groups list - by last activity date, by count of members, count of photos, count of discussions...
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Group categories (something from wishlist) - set of predefined categories (tags) which can be checked when Group is established and then used in Group search (to search for geographical groups, best of groups, people groups, game groups...). I know, it is hard to define reasonable set of categories.
Update 29.9.2011 - Implemented.
Now you can select in setting page one from predefined set of categories and browse groups of selected category only.
Groups content management:
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quick pagination in Add your photo - widget listing users photos makes very difficult to access photos at the end of the list - some slider for quick navigation will be great (I know, you can use your photo pages and tags, but when you want to join new group, widget is only option for selecting photos)
- similarly and generally
navigation through all lists widgets is difficult - this applies for photo and users lists. Hard to get to the end of the list, hard to jump at specific place. A lot of clicking. Is not it possible to add some navigation slider (as option) to widgets and also alternate keyboard interface?
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Search for photos of user in group - At least for group management mode it will be fine to see all photos made by selected group member. This would make easier to maintain the groups with frequent rule "Only XXX photos per user allowed".
Note: This Tip may help
http://www.panoramio.com/forum/viewtopic.php?p=560479#560479
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system support for generic photos max count rules "Only XXX photos per user or per user/day (week, month) allowed". This type of limitation shall be optional part of the group definition and rule shall be enforced by system (thus not allowing to add more photos to the group)
Note: This Tip may help
http://www.panoramio.com/forum/viewtopic.php?p=560482#560482
- if this (very important)
max. allowed photos enforcement rule will be implemented,
consider also transitional state - how to handle galleries/users with more photos than allowed be introduced rule. Hide all their photos in gallery and send them warning? Keep the load of cleanup on the group moderators?
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system support for generic photos min count rules "At least XXX photos per user or per user/day (week, month) required". This type of limitation shall be optional part of the group definition and rule shall be checked by system and triggering alerts to group moderators and owner.
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Ownership transfer missing - I cannot see this function now...
Update 29.9.2011: seems to be implemented
Multiple Group ownership was introduced, so I hope for functional ownership transfer too (I have not tried yet).
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language of "default messages" sent to addressee of invitation, rejection - language shall be based on default language setting of addressee, not sender; or language shall be selected by sender.
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Black list of banned users support - users once banned from group shall not be able to ask for membership again. Access to this black list shall be granted to moderators and owner only.
Update 4.10.2011 - Partially implemented.
When rejecting user asking to join the group, you can check/uncheck option "user can ask to join group again". But list of rejected users (or candidates for rejection) is not visible. And ban option is not available, when you delete existing member from group.
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Forced Moderators/owner messgages and announcements - Moderators and owner shall be able to send annoncement to all group members - regardless user setting of PMs and discussion notifications settings.
Dicussion:
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False "New post in discussion" marker - when thread consist only of my own post
- Problem with discussion iframe load in IE8 - it the group overview, I have a "flash" of generic "connection problem" page, after short delay discussion is finally loaded.
- At the moment I am not sure about problem with loading discussion threads in IE8 - it seems to be fine on my new Win XP installation
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Design of discussions is not clean and does not encourage users for discussion - well, implementation using Google Groups framework provides cluttered interface. Not easy to follow discussions, not much fun to start new one.
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Editable posts in discussions - User shall be able to edit his own posts (typos etc.), moderators shall be able to edit all posts (e.g. maintenance of lists in discussions)
Widgets reliability and functionality:
Some issues with widgets may be IE7 specific, but most of them are general - widgets does not offer best interface and moreover, they
sometimes don't behave as expected. This applies also outside groups:
- Fullscreen photo view only flashes and than show black screen
Update 17.11.2011 - seems to be fixed
- Fullscreen photo starts on first photo in group, not with selected photo
Update 17.11.2011 - seems to be fixed
- After viewing window resize, viewing sequence restarts from beginning
Update 17.11.2011 - seems to be fixed
- Bad memory management of full size view widget lead to blank screen and no response from widget after viewing of some amount of photos (depends on photos sizes and physical computer memory)
- No support for quick navigation in list widgets (quick jump to specific page of widget, to the end, beginning, middle part...)
- Missing alternate keyboard interface in widget lists (scroll left, right, jumps...)
- Scrolling in lists widget sometimes locks (extremly annoying when combined with poor navigation support in lists, as described above)
- List widgets are sometimes blank or list is incomplete
- Non intuitive behaviour of widgets after browser "back" command (context of previous page is not restored exactly, lists are rewinded back to the beginning)
- Widgets are not mobile browsers friendly (e.g. Opera mini)
P.S. I will update this thread in the case I forget about Alzheimer.

P.P.S: Thanks for Groups!
Updates
27.8.2011 - Group categories wish added, remark for max. photos rule transitionsal state
28.8.2011 - General request for widget navigation added, reliability of widgets
29.8. Editable posts in discussions
31.8. Forced annoncements and internal group blacklist of banned users
29.9. Implemented features flaged, workarounds for requested features added.
4.10. Implemented features flaged (banned users)
25.10. List of widget issues extended
17.11. Some WAPI features fixed