Quickly Access : Did you know you can quickly access Skydrive, People, Calendar etc by just clicking on the top left Outlook logo ? This feature will roll out everywhere once, rest of the properties get the same kind of upgrades.
Outlook Status Check : If you think Outlook is not working for you properly, follow this link to find if everything is ok. You can find service status for any other service from Live.
Remember this whole page has gone the redesign keeping in line with the metro design. Notice that you have the Hotmail running in parallel with Outlook.
Messaging History : Did you know that starting with Outlook.com, It is possible to have the chat history saved on the cloud, No ? Good news is that it has been enabled by default for every one.
This option is enabled under Mail Settings > Messaging history. Make sure to enable this.
I am not sure how many tried but you do have a messenger service like Gmail has as quick access on the top navigation bar. Once you click on that, you can chat with any Live Messenger contact and any other third part service like Facebook and Twitter connected with it. The only problem is that it works only with Outlook Messenger and not synced with Windows Live Messenger on your computer. I am guessing that with next upgrades of Messenger, we will see this getting enabled with Live Messenger.
Related Reading : How to sync Windows Live Messenger chat across computers
Social Inbox :
This setting was not there in the Live Settings before and neither was the kind of settings I see here. Outlook is trying to help you interact with some of the connected services directly from the Inbox which can be accepting Facebook Friend Request re replying it from the twitter.
Though this is not something new because I have seen this in Outlook 2010 using the Facebook Outlook Connector but here Outlook is now using the connected service linked with your account. So When you read messages from people you know, Outlook can show extra content from popular social networks and offer other ways to keep in touch.
This also gives you option to control your privacy settings and follows the same privacy settings which you have in your social accounts.You can read more on this at managing your Facebook and Twitter content.