It is possible to have too much stabilization, which is what I think you're asking.
Picture the trajectory of a bullet - a modified parabola. The changes are in the main due to drag - air resistance. Let's keep it simple and just say 'parabola'. Draw in your mind's eye that parabolic path from the muzzle to the target.
Understablized projectiles will of course start to wobble (often when slowing to around transsonic speeds, but in cases of gross understabilization, almost immediately). Accuracy will of course be the pits.
A bullet spun at the proper rate ('proper' of course depending on air density, calibre, bullet specs and so forth), will have its axis on that parabola at any given time. In other words, both bullet tip and the centre of the bullet's base are 'pierced' by the parabola. Such a bullet will land nose-on.
Over-stabilization - It is possible to spin a gyroscopically-stablized projectile so fast that it will maintain the same attitude throughout its flight, impacting the target at the same angle relative to the ground as when it left the muzzle.
OK, you're not going to see that very often with small arms. Don Miller's
How Good are Simple Rules for Estimating Rifling Twist? (
http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_2.pdf) touches on this but correctly notes:
However, stability factors even as high as 3.5 to 4.0 are usually not detrimental to small arms shooting, which is at low angles of elevation ("flat fire").
(The article is pretty technical, but the first page is well worth reading if you're interested in stability.)
Miller notes that problems with higher spin rates (giving higher stability factor) are most noticeable with poor-quality bullets, making AlexF's comments about well-balanced and poorly-balanced tires a very good analogy for real-world small arms accuracy.
Bottom line? Go with Andy's advice:
I suggest you choose a bullet you think will satisfy your needs, and start developing an accurate load. You'll be out shooting, while others will still be debating what should theoretically be accurate or inaccurate.