First of all, you should update to 8.1.3... Then you should check if you have apps like Protube (the ones to download videos and load videos faster) and delete them, they access to the hardware and make the video playback unstable on iOS 8.
You should close all your apps (double click on the home button and slide the apps up), and reboot your phone. You should also check if your iPhone has enough free memory for the temporary store of the video.
If none of that works, you should back up all your data (or upload it to iCloud) and reinstall iOS on your iPhone trough iTunes.