I wanted to mention something in an earlier post but it slipped my mind, so I'll do it now.
There is only one part of a player's body which touches the ground, and only one part which touches the bat or ball.
The hands and/or feet.
I think we're all guilty at some point, I know I am, of trying to see everything at the same time. Watching the pitcher in his delivery while peeking at the infielders or outfielders to see if they're tipping the pitch or anticipating the play. Sometimes we try and keep the pitcher and hitter in our view and using peripheral vision to see if the runner on first is breaking.
I was fortunate as a kid coming from a small town to have our Little League Director be a former minor league player, and also to be in an area where minor league baseball was relatively close. We were all taught when going to a game to watch one player or a smaller area, like the third baseman on one team and the second baseman on the other. Or you can watch the left side of the infield with one and the right side with the other. Maybe the home team pitcher is a fly ball pitcher so you'd watch the LF and CF, and vice versa if he was a groundball specialist.
The point is, you can see more by watching less.
I believe the five tools are physical attributes you are born with and can't be taught; assumed improvements are through technique improvements and repetitive skills. Footwork and the hands both fall into the tools category because you actually throw with your feet. Your hand and arm are the vessels to delivering the ball, but bad footwork more often than not causes bad throws, not a weak arm or poor aim.
What makes a good defensive player is the ability to marry his hands with his feet whether you're a naturally gifted player like Ozzie Smith or have to work hard everyday like Mike Piazza.
This is exactly why we see players move around the diamond with position changes, there is something within their tool or skill set that prohibits them from developing into a major league caliber defender, so the only option the team has is to put him in a spot that negates those weaknesses.
Catching: Catcher remains to me the most important position on the diamond. He's the only position player that can see the entire field, he's the only player outside the pitcher to touch the ball on every pitch and he's singularly responsible for bringing back a pitcher that has lost confidence during the game. These are the reasons why guys like Brad Ausmus and Jason Kendall and Bob Boone had 20 year careers; they were so valuable behind the plate what they did offensively didn't matter.
A catcher needs soft hands, the ability to pick balls out of the dirt on the backhand and forehand side plus catching balls up and out of the zone without losing his balance. He needs to be able to read pitches so as to anticipate balls in the dirt and be in position to make the block. A catcher needs to be able to transition from a defensive position to a throwing position quickly (marrying the hands and feet). A measurement for catcher effectiveness in this area is called "pop time", which is timed from the time the ball hits the catchers glove to the time it hits the infielders glove at second base. Major league average is between 1.9 and 2.0 seconds, an 80 grade pop is anything below 1.7. A catcher with a below average arm can make up time with a quick pop to the bases. A tip of something to watch with catcher's footwork is after he's given the sign and the pitcher is in the windup, when the catcher sets he should only move one foot. I believe a catcher that moves both feet during his setup (other than straight up and down) is compensating for bad footwork or blocking ability.
Footwork is more important for an infielder than an outfielder because he's moving throughout the fielding and throwing process. It's important for a left side infielder to have a strong arm because they sometimes are making plays to their throwing side which has them going away from their target. An infielder should have soft hands which allows him to transfer from the fielding to throwing position and to field bad hops or throws from fellow infielders. He needs solid footwork to move in any direction when fielding and to shift his position when transitioning to the throw. We've all seen guys like Omar Vizquel make a play where it appeared the ball never touched his glove, that's marrying the feet and the hands.
Footwork for an outfielder is important because there is a change of direction involved, but the throwing arm is more important, an average left fielder arm is on par with the strongest infield arm. When scouting an outfielder you want to see carry obviously, but more important is trajectory, how high is the throw and does it remain on a straight line with no fade or sink. A good way to tell if an outfielder has a good release and carry is to watch how the ball reacts after it bounces the first time; a good throw will bounce straight towards the fielder, if it moves in any other direction that indicates a couple of different things but mostly lack of arm strength.
I would always recommend if possible to get to the ballpark early to watch batting or fielding practice. If your starting pitcher is a ground ball machine there may be two or three outfield chances over a nine inning game, but if you get there early you could easily see each outfielder make thirty game situation throws in fifteen minutes. (Same rule applies to the infielders as well).
Next time head to the park get there early and pay attention to the warmups, then when the game starts pick a position or two and focus just on that. I know it's tough, our eyes naturally try and take everything in, but once you get used to it you'll be surprised at how much you see, and that you're really not missing as much as you thought.