If it ain't broke, don't fix it - and while there are many changes that need to be made to Major League Baseball's structure, most have little to do with the schedule themselves. That said, however, while the season schedule does not need a major overhaul, there are a few minor quality of life improvements that can be made to better the season - and a major change to the postseason to heighten drama and make the 162 games of the season just that much more important.
The first change that I would make has to do with the off days; as much as I hate not to have baseball on, more days off, especially during the hot summer months, would be beneficial to the players, and would hopefully keep them healthier by giving their bodies more time to recover from the grind of the season. Games played in northern cities earlier in March or later in November would not be totally pleasant experiences, but all in all, that is a price I would pay to have the players be able to withstand the season's toughest stretches more easily.
A second change would be to reduce travel concerns by scheduling days off for teams that have to travel the day after playing in Sunday Night Baseball or Monday Night Baseball as often as possible, as usually these "getaway days" would be day games. While not a major concern, it would go likely help at least a little bit to reduce the wear and tear on players over the course of the season.
Lastly, the only change that I would make that would affect the season substantially would be to expand the wild card series from a winner-takes-all to a king-of-the-hill format. Right now, there is minimal benefit to having the first wild card, making it easy for a 95-win team that lost its division by 1 game to be eliminated by a 85-win team that barely scraped into the playoffs. While upsets are part of baseball's allure, it would add to the drama (and make underdog stories much more rewarding) by requiring the second wild card to beat the first wild card twice in order to advance, while the first wild card only has to win once. Essentially, this would create a best-of-three series where regular season records dictate the winner of a nonexistent first game.
While these changes would not necessarily change the whole fabric of professional baseball, they would nonetheless help better the product and create a bit more excitement, particularly in the later months. The race for the top wild card spot would gain in importance, and by helping keep players healthier over the course of the season, you are more likely to have your bets players available in October.