I've tried to read through most of these replies, but something that would significantly affect my enjoyment of the game would be more of a role by the coaches. As it stands, coaches play a background role -- and perhaps they always should -- but in real-life a manager can go to his pitching coach and inquire about a player, or perhaps even have his coach speak to a player. This seems complex and complicated, but it doesn't have to be: it can be a simple "click on coach, click on player" and the coach, based on his experience and talent level, can give you an assessment of the player that you've selected. That coach could tell you that a player would benefit from rest, needs to play out of his slump, or totally looks clueless. A pitching coach could tell you that a starter can give you a good effort on short-rest, is tired (in between innings for example, when a player that might normally throw 90 pitches has 65, and winds up tired the next inning), or has a tired arm. Also, in the style of FPS:Baseball, being able to settle your pitcher down during a rough stretch, or just delay the game while you get a reliever warm, would be not only a nice touch, but add to the realism.
Just a thought. There are many times I'd love to have my awesome pitching coach tell me what's wrong with my ace who has a 9.00 ERA in his last five starts (in the form of his "assessment"), or why my star hitter is 0 for his last 54.
Just some thoughts