The eye test thing makes me chuckle. For one thing, most MLB games I've seen in person, I was too far from the field to have anything but a rough idea of what just happened on that play. Thank God for replays on giant video screens!
The other thing is, there's obvious stuff, like a ball going through the wickets or a throw that ends up in the dugout. Pretty hard for anybody to miss. There's also stuff that only a trained eye would notice.