For the Tower Allies category, none of them apart from Eris Morn are unlocked. As far as I know these should have done so as I talked to the NPCs for the first time.
On top of that, I've completed the Crota raid but his card hasn't unlocked either. Although I've heard this can happen if you're not close enough to the kill.
Started playing Destiny after TTK was released.
English
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I've go the same problem; I only have Eris Morn in the Tower Allies section. I also seem to be missing "House of Wolves" Activities cards for "Gone to Ground" and "Ruling House" as reported by others. Tried replaying Ruling House with no effect. Also, I had to replay the Dreadnaught "Shield Brothers" strike twice to get the cards for the two cabal commanders Valus Tlu'Urn and Valus Mau'Ual, though I wonder if that's because I soloed the strikes. Not sure what else I'm missing, I only noticed the the missing HoW and strike cards a couple days ago. The missing Tower Allies cards have been bugging me for quite some time now. My account situation: pre-ordered PS4 version (i.e got the weapons add-ons, and those appear on my add-on list), but didn't start playing until after TTK launched (RL circumstances), started at level zero rather than using the level 25 booster, have not touched PVP with PVP quests relegated to "Abandoned", most of the strikes have only been done once, many of the story missions have only been done once, 1 Warlock up to level 40 (so should have completed the necessary lower level quests), 1 Hunter only up to level 8 and 1 Titan up to level 9 (but I can't remember whether I did a Tower Allies intro quest).
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Oh, and one other account situation: no raids completed; 3 started (VoG, Crota's End and King's Fall) but no progression.