Priorities for Memory in Dominion
Victory Point differential - This should be your highest priority, and is quite easy to remember if only playing two player. If playing 4-player, it is still only 3 numbers to memorize. It is important to know, because it allows you to know if you will win when ending the game.

Everything below is probably more important in some kingdom distributions, and less important in others.

Gold/Silver distribution - What you would really like to know here, is your average treasure value per hand, but that number gets exceedingly difficult to calculate as you consider card draw, victory cards, action cards with variable cash values, etc. It would also be good to know what your opponents AVG hand value is too, but I have a difficult enough time keeping track of my own.

Terminal Actions/2+ Action cards - The number of terminal action cards needs to stay below a certain threshold to prevent you from getting multiple terminal actions in a hand, and being unable to use them both. This threshold is dependant on the number of +2 Action cards and deck size.

Buys/Gains per turn - Important to know if you are losing (or winning), if you can out buy your opponents. 

Defensive/Reaction cards - This is of course highly dependant upon the number of attack cards your opponents have, and how disruptive those attack cards are to your deck.

Individual Combo odds - Highly dependant upon the kingdom cards, but many times you want to be able to estimate the number of Barons/Estates, Treasure Maps, Scout/Great Halls, etc.

Not necessary to count


Deck size
Kingdom card piles
Trash contents