It is interesting to watch the idea of enterprise Twitter evolve right now. We have everything from totally individual (Twitter) to individuals-in-groups-as-a-service (Yammer) to internal (ESME, Laconi.ca and others). Björn Negelman's intro to the subject sets out some of the issues for using this kind of technology inside the firewall.
There must have been lots of startup pitches in the past year that began "it's like Twitter but for ...." and I expect we will see more products and services emerging in this area. Is this a hyped category right now? Well, yes and no. Undoubtedly there is something substantial going on.
As I sometimes shout at panel discussions, enterprise Twitter is a feature not a product; but that is not necessarily the whole truth. It could be a product that catches on to become a category, as indeed Twitter itself seems to have achieved, but I don't believe we have seen it yet. Will Yammer reach Twitter levels of usage (not yet monetisation, note) in quite the same way?
I think the idea of an external service on its own is not enough to capture the imagination of enterprise users. The simple fact that an external service cannot easily integrate with a user's internal authentication is a big barrier to adoption. Also, each colleague has to be found and added individually, which means that network effects will not assert themselves until a critical mass of your colleagues are on the service, whereas an internal Twitter service could simply 'turn on' accounts for everybody, regardless of whether they use them yet or not.
Ultimately, I think it is problematic for Yammer that it cannot hook into the basic internal toolset people use at work, such as AD/LDAP and the internal namespace for links. A good example of this is project teams. If your internal systems know who is in your project team, then this becomes one of the natural groups for enterprise Twitter activity, but right now you would need to recreate these groups each time you use a new externally hosted enterprise Twitter service.
There is also a question of identity. Public Twitter accounts convey personal identity. At work, which is pretty much what enterprise means, people may or may not want to use their own ID or their company/group ID.
This is why projects like ESME and Laconi.ca seem more interesting than Yammer right now, even though Yammer is a good implementation. We are doing a little R&D in this area, partly looking at how an internal Twitter can act as a more flow-based IM, and partly going back to some of the ideas that emerged from last year's LIFT workshop, so we'll see what we can learn. I also expect enterprise Twitter to e a feature that finds its way into various platforms and tools currently being used inside the firewall.

Lee, I think you are right that Yammer has some significant weakness with regards to how it may be adopted within an enterprise. That said, it remains (for me) the closest I have seen to something that is workable. I wouldn't be surprised if they started plugging some of the issues.
With regards to ID, I think that this issue may be overstated as we have been using it within our org for less than a week and have a much healthier level of parcipitation that we have managed to muster for others. As one person put it: "I now have Facebook/Twitter for fun, and Yammer for work!" and "Yammer iPhone app is better than most twitter apps"
Now onto what I see may be it's biggest issue (or possibly a feature depending on how open an org. you want to be). If I have a Yammer account and I leave tomorrow, I could/would still be able to access and participate within the community - cannot see a revoke feature (and by that I do not mean the manual removal of users by admins which doesnt scale within the enterprise). Personally I do not have an issue with this, infact it may help in certain scenarios (work handover, alumni, etc) but not sure how Risk, Governance etc would feel about the intrusions...
Anyway, just my tupence