So what issues are still there? My issue with vanilla was the repetitive grind to get from level 25 to 30. In the end I stopped at 29 because I couldn't take it anymore. Not to mention the bad mission design and laughable story.
Well depends on the various issues you or the person your talking to has with the original game. The restructure of the original missions, for example, is only at the very strictest of definitions a change. So if you expect to suddenly be delighted and amazed with the story it won't happen.
There is still a great deal of annoyance around the lack of matchmaking and various multiplayer choices, which, for many stops them from experiencing any of the better loot stuff because they won't jump in at all due to the same line drawn in the sand about adding an option people want.
Grinding, I personally feel has changed for the better BUT it hasn't really lessened it has just changed forms, and that's fine. No MMO exists without grinding and pretending it doesn't exist lessens the chance of someone enjoying it who is prepared with factual data. You will probably jump to 40 in just a couple hours. I started with a level 25 character and was 40 before 6 hours was up.
Additionally even with the new additions you will, very quickly be repeating stuff. That's Destiny in a nutshell.
And then there are some other issues, I am seeing a lot of crucible complaints and awards but haven't jumped into it enough yet to offer suggestions.
I have always felt Destiny had good shooting now a lot of it has been increased to that same presentation level. Its not an amazing game by any stretch of the means but its good. Competent would be the best word I think. I rated it a Buy but its with some caveats.
I personally don't want to bring it up but there is also the fact that many feel they are paying 100 to get the game that was planned and aren't to stoked about that.