As far as the sparrow/shades(blacksmith cod) you must enter the codes in PSN store! Go the post office/special order and they'll be there! And if there not there than do as I did cause I had the same issue! Close the app then turn off the ps4 wait a few minutes for the Bungie servers to refresh your profile, than turn it on and go back to tower and bam they'll all be there!! :D
As for the emblems you need to go to Bungie.net and confirm them one by one and then close an open destiny so the servers can refresh you r profile again! :)
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Well I'm on Xbox 360 and I've closed and opened Destiny multiple times and they're not there. I might try re-downloading the content, see if that helps.