1. The Win Or Else Mentality.
There are only 2 teams that make the SCF and everyone else goes home disappointed. The NHL Culture is such that we get articles talking about the Oilers being failures and needing "big changes" if they don't win it all. I think it's bad for the game.
I don't know how you'd fix this, but I think if the NHL awarded say the 10th overall pick every year (an additional pick) to the President's Trophy winner, maybe people would care more about the regular season.
I think teams should also get rewards - whether draft picks or extra cap space - the farther they go in the playoffs. Anything the league could do to combat the idea of 31 teams being failures every year would be a step in the right direction.
2. Technology.
Last week the Washington Capitals bought Capfriendly, and it came out that the NHL doesn't like that this information is public.
How dumb is that? The NHL should love that their fans spend hundreds of hours online making trade proposals and making mock-rosters. They could make their own official cap-friendly site and make millions of dollars for themselves but they are apparently blind to this fact.
This is just one example of many. From rights issues with replays and gifs, streaming access, local blackouts, tv scheduling etc. the NHL fumbles technology driven advances at every turn.
NHL.com should have a capfriendly style page, they should have their own trade rumours page, they should have an easy to use GIF builder and archival footage. There are so many ways to use technology to get fans to interact and care about the game it's amazing how badly the NHL is botching it.
Make your own highlights packages, scouting reports etc. People love charts and player cards that show attributes and advanced stats. Basically everything cool that people do without the NHL's authorization, the NHL should do officially instead of trying to ban everything and block access.