I'm using the Osmo Mobile and I don't video the video that is recorded in the Camera Library it seems to be kept only in the DJI Go library. I'm not able to find a way to bulk move the videos either by AirDrop, Wifi or otherwise. I have only been able to Save the videos one at a time to the Photo Library and then AirDrop them to my laptop.
Has anyone else found a faster way?

Same problem: if there is no better way to move the videos, I would not recommend this. I tried hard to find a different way. Not succesful yet. (I am using an Oslo camera as well, so this was meant to be an easy way to take some shots.)
Maybe DJI can tell us, if there will be some software upgrade for this in the future.

This should be an easy fix for DJI. The app has permission to use the Photo Library you should have the option to auto save videos there. Or the app has bulk delete it should be easy to implement a bulk Save.

I'm having the same problem. Spent over an hour with on-line chat support @ DJI and they could not identify the problem. They wanted me to send in the unit for repair... (crazy)! Told them this made absolutely no sense, as the DJI-GO app was working finde in Sync with the Photo Library at the beginning. Tested both an iPhone with iOS 10 an another with iOS 9, but the problem persists. My guess is that some update from DJI-GO app  disrupted the communication with the Poto Library. It's quite annoying having to transfer all the videos and photos from the app to the library.

This issue exists since September, DJI is reluctant to update their users on status. A few weeks ago they stated they are looking into it, but refused to give me any date for an expected fix. Several DJI products are affected by this bug. Very bad for the reputation of DJI! They are not in my column "preferred suppliers" any more.

We're aware of this issue, sorry about it, we're actively working on a fix now.

That's great Thor. Look forward to the fix.

UPDATE -  I've discovered that you can use a software called iMazing for Mac that will allow you to extract videos from the DJI GO App and to a hard drive and then import them into Mac Photos/Camera Roll.

It would be nice to have an option to save photos and videos directly to Photos on iOS so they do not need to be exported at all.  Filmic Pro has this option.

Absolutely agree with all the comments. I am new to OSMO mobile and found it hard to believe that I had to save each video separately to the iPhone photo library. But thanks for the hint to move them to the Mac using AirDrop miketeel I wasnt thinking of that!