Since getting myself an LG G3, I’ve only had one common problem - not being able to play some music from Google Play Music. I had to do a lot of digging to find the solution so hopefully this will help you out if you’re having the same problem.
I found that downloading music to my device, then trying to play it, would produce consistent failures for certain tracks. Some tracks played fine - presumably ones that are owned by me - while others simply spent an agonising time loading before failing miserably. Very strange behaviour for songs that are physically saved on my device.
I first thought it was down to songs being saved on the SD Card, but then the playback was fine on WiFi. This suggested the problem was something to do with my 3G/4G connection.
After doing a LOT of digging, I came across this thread that suggested the settings for the APN were incorrect. For Giffgaff, they should not have a proxy or port. My phone was automatically set up with a proxy and port:
However, these settings are automatically downloaded to the device and cannot be changed. Adding a new APN does not work, as the device is locked to Giffgaff/O2 and wouldn’t let me change it. The only solution was to unlock the phone by paying for an unlock code to unlock the phone and be able to switch the APN. I had luck with that site, with a code arriving in under 20 mins.
Switching to the new APN on these settings solved it. Be sure to leave ‘Proxy’ and ‘Port’ blank.
Now reboot, and your Google Play Music should play absolutely fine. Now you can enjoy ‘Purple Rain’ wherever you want!
I have also detailed this problem on the Giffgaff forums to hopefully fix the default settings.