I checked out the 'Geek's errata after posting last night, and learned that Chuck and I had played a very basic rule incorrectly: In order to dominate a region, you must both control more countries than your opponent and control more battleground countries than your opponent. We had only played with the former condition, not the latter (although we did require both a battleground and non-battleground country controlled in the region).
This would have had a much larger effect on play, not to mention scoring. Huge, in fact. It makes putting influence in France necessary for the US, for example, when in our game Chuck didn't even try until later in the game because he was concerned about DeGaulle. As for scoring, I got 6 points more in the final scoring than I should have, and another 4 when I played the Europe scoring card in the last turn. As such, that's only a 7 point margin, and I'm pretty sure I had the lion's share of dominations in Asia over the course of the game.
The problem was that the reference card had the wrong criteria, although the rulebook is correct. We did play with the correct amount of US influence in Australia.
I suspect that this one change makes the Soviets less likely to win outright, as they will have difficulty getting Domination in Europe without fighting over Italy, and the whole Indo-Pakistani thing (which we avoided by never placing influence in those countries until the late game) becomes more important.
We still had a great time playing, this is only to note that you should check the rulebook rather than the play aid card. There is definitely room on the standard 8.5x11 cardstock aids for this info, I'm sure someone will put out a better copy on the 'Geek soon. I do not think that this has a big effect on the enjoyment factor, but it does make Defcon much more important (in limiting coups, especially in battleground states).