I've copied and pasted some of the common issues/solutions for Windows Live Hotmail on Windows Mobile below. The complete release notes are here.

Time to sync e-mail and contact takes a long time:
During setup for Windows Live for Windows Mobile or when you Switch Windows Live ID, syncing contacts with setup options enabled for "Store Windows Live contacts in your mobile phone's contact list" and "Merge duplicate contacts" can require more than 20 minutes to complete when there are 400 or more contacts.
Corrective action:
Unselect 'Merge duplicate contacts' during setup to improve performance. Do not cancel setup until the process is complete.

Sync fails for large inbox and 400 or more contacts:
During setup for Windows Live for Windows Mobile or when you Switch Windows Live ID, syncing mail with a large inbox or more than 400 contacts with setup options enabled for "Store Windows Live contacts in your mobile phone's contact list" and "Merge duplicate contacts" can appear to fail with the message "Synchronization Fails". No contacts will be available in the contacts application, but the sync process is running in the background and will eventually complete. Until the sync process completes, the device may operate slowly and some functionality will appear to be disabled.
Corrective action:
Do not cancel setup and allow the process to complete. Once the process is complete, contacts will be available in the contacts application.

Synchronization fails when creating and using a new Windows Live ID during setup:
If a new Windows Live ID is created during setup step '2/5' using "Get a Windows Live ID", synchronization will fail at '5/5' and after setup. When synchronization fails during setup, view errors will indicate "Personal settings: Failed to synchronize. E-mail: Windows Live Hotmail is temporarily unavailable. Please try again." After setup the sync status will indicate "Result: Windows Live Hotmail is temporarily unavailable. Please try again." Microsoft has identified this issue and is currently working to correct this temporary problem. The following corrective action is required until the issue is resolved.
Corrective action:
Sign in to Windows Live or Hotmail from a desktop computer and then sign out. Following attempts to synchronize or send/receive mail will be successful with Windows Live for Windows Mobile.

Synchronization fails with message "There is a problem with the server. Please try again later.":
During setup for Windows Live for Windows Mobile or when synchronizing e-mail, synchronization may fail with the message "There is a problem with the server. Please try again later." If this issue persists, it is likely to be a known problem where at least one e-mail in the inbox prevents the completion of the synchronization. Microsoft has identified this issue and is currently working to correct this temporary problem.
Corrective action:
From a desktop computer using Windows Live/Hotmail, move e-mail from your inbox to another folder and then trying synchronizing e-mail on your device again. If the synchronization is successful, one or more of the e-mail messages that you moved to another folder prevented the completion of the synchronization. If you wish to move your e-mail back to your inbox, you must determine the specific messages preventing synchronization and move each message to a non-sync folder or delete it.

Bill,

 I want to uncheck the option "Store Windows Live contacts in your mobile phone's contact list" but it is checked and grayed out --- I just can't uncheck it. I simply don't want the email contacts to be mixed up with my phone contacts since they are so many that render the "contacts" unusable. Can you help me please?

Alvaro

Hi, alvaroneder, and welcome to the Connection. I don't have Windows Live set up on my phone at the moment, so I can't try this myself, but my first thought is that you may need to delete your Live account and then re-create it, being sure to uncheck the contacts option when you re-create the account. This may be because with your current setup, you have already pulled all your Live contacts down, and WM can't remove them from the phone unless you remove the account completely. Is this an option for you? Let us know...

To delete a Live account from your WM phone:

Open Windows Live in Start - Programs on the device. In the Menu, select Account Options and select Switch Accounts. This will remove all emails from your device. When done, the EULA page will appear. On that screen, make sure you select REJECT.  

Hi,

I never had any errors during setup but now I'm contantly getting the "Windows live hotmail is temporarily unavailable" message. If I go into my windows live sync status it says "E-mail: Failed to start synchronising" I've set the sync schedule to "as items arrive".

It does pull my emails down every so often but it's getting quite annoying having to keep dismissing the message, any ideas?

Welcome to The Connection, Louisa - please could you first try soft resetting your device. Depending on your device, you may need to remove the battery to do this.