First thing they need is a breakout scheme and more structure. They were systematically either throwing the puck up the boards or throwing it to an empty area, and the Rangers feasted on such predictability. That in my mind is the number one problem facing the Habs.
The number two problem is zone entries -- all that dumping and chasing leads to the opponent having the puck more, which leads to the team defending more, which leads to defensive breakdowns. Hockey's not a two-mode game, and part of the reason the Habs had such trouble on defense is because they also had lots of trouble on offense (and vice-versa).
Personnel-wise they need a good, mobile, skilled top-4 RD, and that's their foremost personnel need. Emelin was unable to fulfill the role they gave him. He might have done better on his good side, but he has to be considered a trading piece at this point (his size, thwackiness and KHL credentials will make him attractive to gullible GMs). The Habs would have been better-served using Diaz in that role, really, but ideally they need to do better than that.
Better personnel usage wouldn't hurt. The most positive thing about the playoff run may be the change in narrative around Subban's maturity. Maybe they'll stop yanking the chain on the team's best player now and actually use him like the elite D-man he is. Not populating the third pairing with pylons wouldn't hurt either.
One big key to a strong team and what makes the top Western team so good is how much skill and mobility they have on the blueline. The Habs should build towards that model and avoid the trap of the "stay-at-home defenseman". Many of them are actually pretty crappy and get carried by a superior puck-mover. The offensive/defensive "complementary" pairing is a trap.
But if they don't have a good structure, they can put whoever they want back there and they'll keep sucking. The coach needs to change the tactics or the GM needs to change the coach.
