There a few notable features that will not work properly for uses who don't work with Windows (or, to some extent, Windows users with Firefox).
- Most importantly - you cannot check out and edit documents directly from the browser, or save them into SharePoint. (You can edit them in-browser using Web App though, which is probably better for Linux users anyway, to avoid compatibility issues).
- Datasheet view will not work.
- Explorer view isn't supported ("Open with Explorer" on 2010)
- The upload multiple files isn't supported either (that means they are pretty much limited to uploading one file at a time)
- Outlook integration - There are RSS feeds, but they are not as good as the way Outlook handles SharePoint lists (most notably Task lists and Calendars)
A official, comprehensive list can be found on TechNet: Plan browser support (SharePoint Server 2010)
The next part of your question regards site administration. The lack of batch operations means there are some limitations on users, but for most tasks, they should be OK.
Central Administration shouldn't be a problem (it is a site, and can be accessible from outside of the central server), but why would you have people there anyway? Another obvious administrative limitation is not being able to use SharePoint Designer.
In all cases, we try to make our sites as compatible as possible for all users, but not for all administrators - an administrator can RDP into another computer if needed, or switch temporary to Windows if that what it take to do their job.