Can not delete individual messages from iMessage I do have the same issue like Wanda. I did restart the phone many times. Still the "trash" bin does not appear on the bottom page. And that's not only on my iPhone5, but also in the iPad. This problem started once I did update to IOS8. 
Together with some slow reaction from my devices. 
No idea how to fix it.
How to delete individual messages changed a little as of iOS 8.

Hold your thumb on the message, until you see the "copy | more" bubble and pick "more" then you will be able to select messages individually and trash them.