A palate cleanser from my discussions of two candidates I can't stand.
To me, the main purpose of replay is to prevent gross injustices in officiating decisions. Things like the Don Denkinger decision in the 1985 World Series.
In particular, we want to prevent a player making a great effort, and getting screwed over by a bad call.
In football, the plays reviewed are generally plays of skill. Did the receiver keep both feet in bounds? Did the runner fumble the ball before the going down? Did the ball carrier get the ball over the goal line? There's some luck involved, but these are plays of skill.
In basketball.... not so much. Sometimes reviews are used for things like buzzer beaters. But more often, it's for determining who the ball deflected off before going out of bounds. This is almost always a matter of luck, not skill. Getting these calls wrong can be chalked up to a "bad break" rather than an injustice crying out for redress.
Now, in baseball, a common application is to ensure that baserunners who slid into 2nd or 3rd base maintain contact with the base throughout their slide while getting tagged. As Dave Cameron notes, if this is measuring a skill, it's one that has never been crucial in the history of baseball, and is only measured thanks to the new technology.
Is this a positive innovation? Well, assuming that sliding such that one never comes off the bag isn't something that can be easily picked up, the effect of this will be to drive down stolen bases and runners going for extra bases. Which are the more exciting plays in baseball, attempted by exciting players. Baseball needs more of these plays, not fewer. And these are not inaccuracies that are noted in real time.
There are more dimensions to justice than just accuracy. When Dustin Johnson played the final round of the US Open unsure if he had a penalty, that was an injustice, regardless of whether they got the call right.
Getting things right is an admirable motive, but in some cases, it's probably best to trade some accuracy for speed.