My recently purchased 04 Miata has the famous 65mph shimmy, though it seems worst at 70-72mph. I bought the car anyway, just because it's so perfect in every other area I figured I could live with it if I had to.
I mentioned the problem to one of my co-workers who has a lot of muscle cars and the first thing he mentioned to me was if I had locking lug nuts, they should be lined up with the valve stem, since it is the lightest part of the wheel. I'm not sure how much heavier a small, thin patch of aluminum would be compared to a valve stem, but none of the lug nuts were lined up that way and I changed them. If it made a difference it was very small.
Next I came across this page
The problem now is the tires. They only have 17k miles on them. I'm not sure whether to replace the one, replace them all, or what. The vibration really isn't that bad now, and as long as it doesn't return I can probably live with it for a while.
Anyway I just wanted to report that the matched balancing and alignment made a noticeable difference in reducing shimmy. The car is even closer to perfect than it was before.