How can I get a video *into* the photo/video gallery on an iPad or iPhone?
I'm surprised nobody has answered this correctly.

The solution is to open iTunes, click on your iPhone, go to the Photos tab, then Sync Photos for the folder that contains the photo and video subfolders you want to sync.  Each subfolder will then be sync'ed to your iphone UNDERNEATH the Camera Roll as new Albums, and these are treated seperately than the Camera Roll and will always remain synced.

Furthermore, apps that can access the Camera Roll almost always can also access Synced Albums, so this should really work well for you.  I keep a whole bunch of old photos and videos on my iPhone at all times using this method and it works great.

As a bonus, unlike the Camera Roll, these Synced Albums don't get backed up in iTunes, so it won't slow down your Backup like a growing Camera Roll will.