Hi GuyWalksIntoABar,
I have the same problem either. On 29 July I migrated "my mail only" from MobileMe to iCloud.
Thanks to Roger Wilmut1 kind and most helpful advise (many thanks Roger!) ho to configure my Mail app manually in Tiger http://www.wilmut.webspace.virginmedia.com/notes/icloudmail2.html I managed (with some difficulties) to make at least my mail Mail working normally (almost) on Tiger 10.4.11 but additionally I entered my aliases (Mail, Tiger) as Roger described here for Snow Leopard http://www.wilmut.webspace.virginmedia.com/notes/icloudmail.html
So - my aliases work ok - I can send and receive e-mails - but only when I use Mail app. When I log to my iCloud account at www.icloud.com/#mail/prefences/acounts I see no aliases at all. The box is empty - it says that I can create up to three aliases... I have five aliases - .mac.com and the version of them .me.com but I use my .mac.com only. I did not try to 'recreate' any of them in that 'alias box'.
Logging to iCloud tested on:
Mac - Tiger 10.4.11, Safari 4.1.3 (there is an info: "browser unsupported" but you can log in without any problem) and PC (hmm some Dell machine Windows 7) - latest Firefox (here "all is supported" but an alias box is empty either).
So I think that it is not the browser fault but it must be the iCloud issue...
Hope they will fix that great inconvenience. I am with .mac from iTools through .mac and MobileMe - about 12 years and I have never had so such stress with e-mail...
Cheers