To temporarily correct the issue and see the actual status of the message (read or delivered), close off the Messages app from multitasking (double-tap Home, swipe Messages up & off the screen), then either power-cycle or force-restart the device (see below). Afterwards, open/run the Messages app again. The correct message status will then be displayed. The work-around is to never close off the Messages app from multitasking and then re-open it since this is when the read/delivered issue occurs.
Force Restart (won't affect settings/data/music/apps/etc)
1. Press and hold the Sleep/Wake button
2. Press and hold the Home button
3. Keep holding both buttons until the display turns off, then back on displaying the Apple logo.