When my iPhone runs out of memory or storage I usually back up my pictures and movies with the Preview or Image Capture apps that are built in my OS on my MacBook Pro. Lately I noticed that the delete button is greyed out (or is it grayed out).
The problem is iCloud. When your phone begins to notice you are running out of storage space it will ask you if you want to turn on iCloud to free up some space. Once you turn on iCloud you are then unable to delete files off your iPhone with your Preview or Image Capture apps.
So the solution is.
1. Back up your picture and videos from your iPhone.
2. Turn off iCloud for pictures and movies
3. On your iPhone click the home button then click, settings, yourname, and icloud. The turn off iCloud Photo Library. You will get a message about removing photos and movies off the phone (which is why you backed up before doing this step.
3. Use Preview or Image Capture to delete the pictures and movies you do not need. If not doesn’t work you will need to unplug your iPhone from your matchbook and plug it back in.