First, congrats on getting the Best coach on the market, was just time for a shake up/change with the Canucks. There has been some good stuff posted on the way AV approaches the game already so I will not add to much, just ignore the haters since AV will prove them wrong...
All ready been said I would say, But AV line juggles like no one else, make of it what you will but as a fan you will need to deal with it
Break outs were broken for the last two seasons I would say, but when they were doing well AV liked a good quick transition and in the 2011 run that transition was as quick as they come
of late when the D gets the puck in there own zone they would pull back and try and get the fore-checker to come up, creating a gap, while sending all three forwards up the ice then they would try and use they space and try connect with the open player. This was fairly well scouted in the west and teams were happy to hang back or send in two for checkers hard so all our D could do was hide behind the net and ring it around the boards for a tip in.
the drop pass was used a lot, I would guess as a way to beat traps, this was also well scouted and I feel teams new it was coming so they would set a trap and have a guy floating for the drop pass, LA sure did in 2012...
when defending in our zone instead of try and clog up the shooting lane and block shots, the canucks were happier to try and keep the puck carrier on the outside, and tie up passing lanes, allowing the puck carrier to have a "free" shot from the bad angle with the goalie seeing it all the way.
offensively I will be interested how he sets up with the rangers next season, with the canucks he had them set up a cycle most of the time, but that has alot to do with having the twins, and also no players that would try and get into the slot. also a lot of the plan for offence I think was to give up a bad shot and try and use speed and quick transition to counter but after 2011 we seemed to try and keep the game tighter (or lost that quick transition for whatever reason) and that dried up our offence I feel.
one last thing, It was no secret that the canucks were a better team when they out hit there opponent, in the 2011 run there was a stat that had our chance of winning increase a lot when we out hit the other team, and often we would outhit them by a wide margin.
Hope that helps and adds something to look out for, just my opinions, others may disagree