There may be an aggregated email that may be sent to me that allows me to quickly invite friends from gmail.com, facebook, twitter or other email. I don't want to think about friends' email addresses when I invite them. ;)

If fact is public, make it have options to be shared on other social networks.

This will work for small groups GOOD.
I.e. i'm a team lead in some company, i want to "appreciate" some user with title "worker of the month", or "best tester of the year", or "killed N bugs at work time", etc.

And users can see facts about themselves only in this group.

RESTful API or just a downloadable CSV dump will do. Personal information should not be "trapped" within a service. See http://dataliberation.org for hints.

I would like to have a facts badge on my blog. Something similar to http://developers.linkedin.com/plugins/member-profile-plugin

It would be nice if we can comment on friends' facts. :)

When someone confirm/like/comment my fact, it should show notification about that (same as notifications in facebook)

Also super feature will be to have direct access to notifications at any time, not just when there is new notifications.

It is interesting to watch a fact type and get notifications when top user is changed in the context of that fact type.

For example, it was known that Marat pressed 100kg, but it was interesting that there is a new person who pressed 140 kg (of course if I am interesting in pressing). I would like to get somehow a notification (on the website) that in that group (who is pressing) we've got a new records-man.

It is a "must have" feature for any service that sends e-mails.