How and why does spinning a bullet make it stable?

What we have here, is a failure to communicate.

Does spinning a bullet entail some inaccuracy/deviation? Doesn’t making the bullet spin one way make it steer that way a bit?

Purely accuracy-wise, which has the greatest potential: fins, spinning or heavy front combined with light rear?
Say you had a hollow bullet* and put fins inside it, could they stabilize the bullet or would they have to be outside to have any chance of providing sufficient stability?
*Like this: http://i381.photobucket.com/albums/oo255/FEDE_EL_SOMALI/67654.jpg

No. The axis of spin is in the direction of travel, so it doesn’t make the bullet curve one way or the other.

Imagine a bullet spinning clockwise (from your point of view) while it heads away from you. The spin causes the top of the bullet to move to the right and the bottom of the bullet to move to left. Any lateral force caused by the spin on the top of the bullet will be counterbalanced by an opposite lateral force on the bottom.

Bacause the bullet flies in an arc the spin axis is always at a slight angle to the direction of travel. The angle is slight so the drift due to Magnus effect is small and really only noticeable at extreme ranges. The drift is to the right for the usual twist direction. Ladder and vernier sights are sometimes canted ever so slightly off vertical to compensate, but unless the wind is dead calm it is hard to get the cant set right.