I am very much in favor of replay for everything except balls and strikes. Home runs, fair/foul calls, safe/out calls on the bases and at the plate, and all the other little things that don't come up often (catcher's interference, contested HBPs, et cetera). A lot of noise has been made by people about the integrity of the game and the value of keeping baseball the way it has always been, but I don't really see any benefit in that. As far as I can see, the major arguments are these:
1. Baseball should not be changed dramatically.
Well, this one is ridiculous. I am a huge proponent of the preservation of important ideas, achievements, and historical landmarks. I have already made it clear on this site that I would never support, for example, the demolition of Fenway Park. However, I believe that the best way to continue pushing baseball along with us into the future is to keep a balance between the old and the new. Batting helmets, home run replay, free agency, and a dozen other changes to baseball both on and off the field have taken place between the creation of the major leagues and today. Each one has been accompanied by a ludicrously hyperbolic group of "purists" assuring us all that these changes would represent the beginning of the end of professional baseball, it's popularity, and possibly the universe itself. Thus far, unsurprisingly, that has not happened. Forgive me for getting Trekkie on you, but the Federation government has strict regulations regarding the preservation of historical buildings. Some are still around by the 24th century, and yet many have public transporter stations built into them. That is what baseball needs to do. Mix the old and the new. Preserve the essence of this great game while not letting it get swept away in the raging river of progress. As long as the baseballs remain the same, the bats are still made of wood, and it's still being played by human beings, I see absolutely no problem with implementing technological advancements. It can only serve to keep baseball part of the 21st century.
2. It will slow down the game
I don't know if anyone has noticed, but baseball is slow. It is always slow. Between coaches and catchers visiting the mound, pitching changes, pitchers taking their sweet time, time-outs, and occasionally naked people running onto the field and taking selfies (I swear, the voices told me I would be rewarded!), baseball has been, is, and always will be much more slowly paced than nearly any other sport. (I'm looking at you, soccer. f*** you, you suck). Home run replay has been in use for a few seasons now and it has not noticeably corrupted the smooth flow of a baseball game. It has not even been used during every game. Retrosheet has a list of every reviewed HR call since the creation of the rule and it is barely a fraction of a percent long as the list of games that have been played in the same timeframe. Even replay of every disputed call during a game would not add more than a few minutes to the length of a game. I think we can all agree that five minutes added to the game's length is a more than adequate consequence to making sure the correct calls are made.