Android music pauses when using headphones
Are your headphones defective or have a weak spot? You can try a couple of things, such as testing this on another Android device. 

It could potentially be the ROM and its ability to detect headphones properly while doing different things (Multi-tasking in a sort of sense). 

What you can do is go into Settings and turned Motion off. Sometimes it can sense movement and such and it'll pause accordingly. I'll look into this more but into l your next response, this is what I have to say. 

Update

It is probably an Android 4.2.2 issue. You can downgrade, wait for an upgrade or perhaps install the 4.3 KitKat ROM.

Other options are trying newer/older versions of the Google Play Music software.