I've complied this list over a while of just random thoughts that popped to me; now, I'll post it here. NOTE: these are all GM Mode related:
-- pick staff based off grade and pay them. Your owner gives you a cap to spend on staff.
-- converse with your owner on expectations through the season. Converse with players throughout about the on-ice play, coach, systems, playing time. Converse with your coach on expectations, including setting certain expectations for certain players (using Galchenyuk as an example: telling Therrien you want Chucky to average 17 mins a game, you want him in the top-six, on the PP and to slowly start developing his defensive game to build him into a strong two-way player. For Pacioretty, I would tell him I want him on a certain side on the PP and for him to play in every situation.).
-- when conversing with players, you'll also have a meter where it shows how they react to the coach and his systems and who's happiest and who's not. You'll also get a meter for the feel of the locker room and how the players react to the leaders.
-- if certain teams have an internal cap, the owner will let it be known to the GM. Also, if that team is having a good season and/or can afford it because there's more people at the games, the owner will notify the GM (you) to spend up to the cap for a strong run.
-- in-depth scouting. This goes back go the staff-grading system up above. If you have a lower grade scout (who will be cheaper), you'll get a very bare bones analysis of the draft and player types and you'll be less likely to find late-draft steals. Higher graded scouts will provide more in-depth analysis and even find you late-round gems. They'll even give you certain information on certain players (so-and-so is strong on the puck, has a good hockey IQ, but player development will need to work with him to improve his defensive game. He has the potential to be a top __ player.). Something like that to add a new element to the draft and scouting.
-- if choosing a team who doesn't have a big budget to start, you'd need to decide how to spend the money on staff. Are you okay with a cheaper, less experienced coach in order to get a top-level scout to build for the future? Do you want an expensive, good coach to win with your team as is, but sacrifice the future in doing so?
-- EA now has the NBC licensing? Why not get some coverage to go with it? Maybe even get McKenzie, Dreger, McGuire, etc. for the deadline and draft day to analyze moves and draft picks. Also, make these days big events! More trades. Have teams flat out make themselves a seller or a buyer at the deadline.
-- actually calling teams to negotiate trades like in NBA 2K15. You can let the other GM know why a deal doesn't work and they can let you know why it won't work aside from the tired old message that always comes up now.
-- interviews with the press. Real GMs do it. Address the press about the team and its needs, and everything you say has some sort of affect on the roster members of the team, coaching staff, and the owner, whether positive or negative. In NBA 2K15, a press conference is called after whatever trade you make or any other type of event.
-- let me communicate with my players!!!! Ice time, spots, troubles in the locker room or with the coach, let me communicate with them! If a player is unhappy, demands a trade, is tired, whatever, let me talk to them.
-- on the tired/fatigue thing, if that is the case, I simply tell the coach to ease up on his minutes for a few games.
-- management, chemistry, coach likability meters. All these will affect the team. The lower they are, the worse. The higher, the better the team will be. Edmonton, as it is in these games, are always good in GM mode only because of their roster. We know in real life that that's not the case and management, culture, chemistry and coaches play a big part in this. These meters would add a sense of realism to the mode. Calgary, in real life, is playing much better than their record says they should, because of their coach and the culture in the organization.
