This is weird. I just updated to iPhone 5 (restored from 4 backup) but this happened on my iPhone 4 too.
Mail comes in - iCloud email. The iPhone makes it's mail recieved sound, but the mail is not displayed becaue the iPhone has marked it as read. And if I open Mail on my iMac (Moutain Lion) - the email is not highlighted but marked as read too. BUT - on my iPad Mini (also new) the email is NOT marked Read and the Mail icon lists 1 new message. And it is also in the Notification center. But the iPhone it is not in Notification Center.
This was happening on my 4 too - but not all email. AND Not always the same email. Sometimes the email that is marked read - comes in normal at times.
If Mail on y iMac is open - these emails come in and are not marked read. So it appears the iPhone (4 & 5) is the culprit.
Any ideas or thoughts?