Here is a quoted post from the Mozilla forum.
It does not directly answer the problem, but the highlighted part may be of interest.
Microsoft Team.. wrote:
Hello Stephen,
Thank you for writing to Windows Live Hotmail Technical Support. This is Ricky and based on the service request that you have provided, I gather that you are encountering a message that is asking you to upgrade your browser. Also, you are unable to view your account using the full version of Live Hotmail. I understand the importance of having this addressed immediately and I will do my best to assist you.
We need additional information from you in order to find the cause of this issue. It will help our investigation if you can provide us with the detailed steps that you have performed when you were prompted with the message to upgrade your browser.
In addition to this, please send us a screenshot of the error you are encountering when trying to navigate your Windows Live Hotmail account. For your convenience, I have provided the steps below on how to do this: then click on the "Save" button.
<snip .. Windows instructions that take 5 click in Linux>
9. Click "Send."
You can also send the screenshot to our test account at WLMTestMsg AT hotmail DOT com. If you prefer to do this, please put " ************ ID " as the subject of your e-mail message for easy tracking and let us know once you have sent the requested information by replying to this e-mail.
Moving forward, for your concern on not being able to access the full version of Windows Live Hotmail. please be guided that Currently, the full version of Windows Live Hotmail is not compatible with Firefox 3. We have identified the cause of the problem and are diligently working with Firefox to resolve the issue. This is expected to be resolved in the next release of Windows Live Hotmail scheduled for later this year. In the meantime we suggest the following workarounds:
1. Use the basic version of Windows Live Hotmail
2. Downgrade your browser version to Firefox 2
3. Install IEtab(add-on):