The dynamic nature of the MMO genre has yet to be fully realised in Destiny. It is always evolving, always adding something new or offering something unique for players to try and Destiny could definitely use a constant flow of unique ideas and concepts. Limited time events are a good start (the Iron Banner is especially enjoyable when it rolls around) as they bring players back into the game but permanent additions will keep those players sticking around for longer. A popular idea is a game mode where players race their Sparrows (small hoverbikes owned by each player) across the various maps of the game; it's really not a bad idea at all, especially given how pretty a game Destiny is. The Crucible could also use some newer ideas and modes: Control and Clash are growing pretty repetitive now. How about a Capture The Flag variant? Many of the game's maps are perfectly build for CTF gameplay and it would offer something different for players. Trialing the idea in a limited time event seems like a smart move to gauge popularity. Outside of PvP content, there's some great ideas which Bungie could work with too. The platforming sections in Destiny's raids proved to be a popular addition, so it might also be worth exploring game modes which would test players' jumping abilities and skills.
I have an addiction to achievements, a craving for new bands and a dream to become Captain America. I once finished second in a Mario Kart 7 tournament so I'm kind of a big deal.