Paul, uhmmm this maybe hard for someone that is just getting their feet wet in the game, I was thinking of a desired checklist too, how about developing the thought process: familiarity concepts, and pattern recognition,

Playing blindfolded is the best vision exercise. You also save money

since you do not need pieces or  a board.

I'll try to desribe my thought process during some of my games. (Note: I'm not the best person for board vision, but I try) 

Here is a position I had recently in a game. Before I moved I looked at all forcing moves (Capetures, checks and threats) in the position, all hanging pieces and how the pawn structure could change. A: The capetures are dxc5, exf6, Nxd5, Qxe6, Qxe6, Qxg7, Bxh7. B: The checks are Qh5+, Qg6+, Bg6+. All though some of these moves are straight out blunders I analyse them cause they are short analysis and won't waste that much time.

A:

1. dxc5 allows him to improve the position of his night, or Queen, he can also ignore the pawn and play, fxe5.

2. exf6 allows Nxf6 attacking my Queen and improving the nights position.

3. Nxd5 gives up a night, but in some positions like this Nxd5 could be a winning tactic.

4. Qxe6 gives away a whole Queen, but it's good to notice that e6 is week.

5. Qxg7 also gives away a whole Queen, but g7 is another potentual weekness.

6. Bxh7 creates a pretty tactic if Rxh7 is played, the reason I didn't play this cause the position is opening up, while I'm trying to take pawns with tactics. I didn't want to involve my king in these analysis.

B

1. Qh5+ black replys Qf7 and either wants to exchange Queens (Good for blacks crampt space or else whites move looked bad.

2. Qg6+ gives away a queen, but there are tactics when this queen sac will work.

3. Bg6+ gives away the bishop and after ...hxg6 and Qxg6+, Qf7 is played.

Now that I've looked at all the captures, I look at all the hanging pieces, which is my b2 pawn and all the rooks. It's good to notice the b2 pawn, cause this pawn becomes a target fast, and one should know if it needs protection. 

Now I look at the pawn structure (Which would normally the center pawns). Since my pawns are all on the opposite colours to my bishop I am said to have the superior minor piece, but because there is a lot of pawn tension, the position has the potentual of changing.

After looking at all these things in the position I decide on a short list of cadidate moves. Here was my list

1.Bxh7 I decided not for the reasons above.

1. dxc5 I thought about this move, cause white is threatening to win a pawn, but I stated the reasons above.

1. Ne2 I might have played this, were it not for c4

1. 0-0 Sould I just castle and see how black continues

1. 0-0-0 Sould I castle Queenside putting a rook on the open file.

Now after all the above I decided to castle kingside. I spend 15 minutes deciding on this move.

1.0-0 cxd4

2. Ne2 fxe5

3. fxe5 Ndxe5

4. Nxe5 Nxe5

5. Qh5+ Nf7

After this move I played something horrible which I shall not show, but Bxh7 is a strong move, cause black won't be able to tack advantage of the pin. Blacks position is difficult to play after there moves.

More importantly - how do you get x-ray vision?

I would love x-ray vision. This might not help me in chess, but it would help me when I'm walking down the street or if I'm in a game of poker.

I don't know if there is a specific tool that will help you learn to not hang pieces, but one of the big milestones in developing past a beginner Chess player is to stop looking exclusively at your plans, and start considering what your opponent might do.

If you look at the board from the other guy's perspective, a hanging piece on your part will jump out at you.

You'll also save yourself some back rank check mates.

Board vision is similar to but not quite the same as tactics.  from a didatic point of view there is a difference. Its not just calculating tactics its about seeing the whole board. As I mentioned before , and I too was critical of the concept , chess mazes! Even for experts and masters they are a lot of fun. A GM I know grabbed a copy of the book and used it for endgame training.