Just some experience:
I don't own a Mini, though I know a number of people who do, and have shot with and/or coached them on their shooting. This has allowed me to see 6 or 7 different Minis in action.
The Mini-14 *does* have the accuracy problems that it's known so well for. However, it would seem like a surprisingly large percentage of its inaccuracy comes from the poor fit of the wood stock. The models with the factory synthetic stock have been noticably more accurate, generally between 2 and 3 MOA with ammo they like.
With this in mind, I recommended the Choate synthetic stock to a friend who was about to sell his wood-stocked Ranch due to his frustrations with its inaccuracy. WHAT A DIFFERENCE! The Choate fits the action even better than the factory synthetic, and accuracy down in the 2 MOA range. That's a BIG difference from the 6-8 MOA that I've seen him get from a 100-yard benchrest.
Yes, the Mini will still string rounds when the barrel heats up, and still has "first shot" variances. But if you already own one, and are generally happy with it, and are willing to trade the wood stock for a considerable accuracy gain, try a synthetic stock, preferably the Choate. It may give new life to your Mini too...
-Troy