Just to clarify — while there are various people experiencing various issues, the core original issue is a local one, not network related.
That is, when people read their mail in Apple Mail on mobile devices, the mail is not being marked as read.
We've observed this in cases where people only have one device, and where their only mail account is their Apple mail account and they're using the device and Mail "out of the box" with default settings and a new Apple email account.
So this is likely either a bug, or an error in design and implementation.
It's not likely to be a user error.
In the cases we've seen where users have multiple devices, when the mail is manually marked as read on one device, user's other devices do update the read/unread status correctly. Again, this suggests the issue is local to the device.
The fact that that there are users who aren't experiencing the problem isn't particularly relevant — very few bugs or design/implementation errors affect all users.
I'd recommend that all people having this issue or a related one take the additional step of reporting it via the Apple feedback submission form.
Cheers folks
T.