For some reason, PSN has been more or less the ones having problems. It is more than likely just that the PSN is overtaxed with numbers from Destiny, you know, too many people on the servers. This is something that will get fixed- it won't last forever.
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Both xbox 360 and one are having countless problems. Not just PSN. I can't play the game at all on xbox one. Reinstalled 3x so far. Not doing a fourth yet until there's some sort of response from bungie or xbox about something.