I had the same issue. Could only play the first mission then got the "installing 15%" message. Main Menu screen said 100% installation, full game 30%. Heres what I did.
1) in the ps4 menu I went to SETTINGS --> PSN --> RESTORE LICENCES. I restored all licences.
2) Inserted BF4 disk and played the campaign from the last checkpoint.
3) when I reached the next checkpoint i got the "installing 15%" message and it took me back to the main menu.
4) I just left the system on and left the disk in an on the main menu.
5) I looked this morning and it is at 85%.
Its not there yet but its better than seeing 30% every day.
Make sure your power setting is set to not shut off or go into sleep mode. I'll update later. Good luck.
