We have several issues that need to be addressed when it comes down to HL. This is supposed to be the competitive mode of Heroes of the Storm and right now it simply does not fulfill that function. Here's a couple of things that need to be done imho:
implement hero swaps during draft so people can draft properly
crack down hard on leavers and feeders
educate the playerbase better, they currently "learn" the game in QM and are then completely lost when they head into HL (mostly because of the random QM teamcompositions)
better promotion for HGC within the client so the more casual playerbase can learn from the pros
bring back PBM (and this time make sure to make it more transparent how it works so people don't get confused)
some form of either MMR or Ranked Points decay
better incentives to play (especially on the GM level)
make the opponents player-names visible again AND allow for profiles to be checked during draft (= more transparency instead of less)
For leagues lower than Masters I'm also a huge fan of getting rid of promotion/demotion games outside of a complete tier-change (aka. no demotion/promotion game between for example D1/D2/D3, but only for B->S->G->P->D).
Just a few thoughts. I could go on about this topic for ever but I guess I'll leave it at that. Hero League is supposed to be a competitive mode and ideally should be the bridge between competitive amateur play and the pro-scene.