I'm not very impressed with Google Groups in general. For personal discussion groups they seem fine. But Google also sells Groups as the feature to replace mailing lists in Exchange. I've seen all kinds of weirdness when Groups is combine with calendar invites. Sending an invite to the group address (very common thing to do with Exchange) results in an e-mail message at gmail.com with two separate yes/no/maybe links. Clicking one set returns errors that you aren't on the invite, while clicking the other works. Problem is, the working set of links only shows on gmail.com, and is not propagated to IMAP users, iOS users, Android users or Blackberry users.