I have the same issue:
1) Sign in to icloud mail (icloud.com) via my chrome browser (latest version)
2) Click on an email to look at the contents, or hit reply
3) Briefly look at message saying "Cannot mark mail as read. ...(second line I cannot read fast enough)..."
4) Be presented with the icloud login screen again. (Repeat step 1...)
I have rebooted the entire machine and tried Firefox browser. It does not seem to be a browser issue, but an icloud server issue, as my action sent back to the server causes it to log me out.
So I have no email access on my PC. I have used my phone for some emails, but I need the full web interface to properly function.
Apple? Anybody? What can I do besides wait for it to get fixed?
Thanks