The old M16s of the Viet Nam era had twist rates of 1:14" and it would not stabilize the M193 55 gr FMJ bullet in low temps. Because all bullets with the shape of a spitzer have a tendency to tumble and the lack of sufficient twist, the M193 bullets would indeed tumble and sometimes wouldn't get to the 100 meter target. Here's a copy of a teminal ballistics commentary:
TERMINAL BALLISTICS
There are two different aspects to this; the effect of projectile strike against soft targets (animals or people) and the effect against armour.
First, against soft targets (the squeamish have permission to duck this section!). A military (i.e. fully jacketed, pointed, non-expanding) rifle bullet will be destabilised when hitting a soft target and will tumble. This is because its shape means that the centre of gravity of the bullet is towards the rear so it naturally prefers to fly base-first. Spinning the bullet by means of the rifling keeps the bullet flying point-first through the air, but flesh is about 400 times denser than air so spinning is no longer enough; the bullet destabilises and turns over to travel base-first, a process known as tumbling. In so doing it obviously inflicts a far more serious wound than if it carried on flying straight through the body. Incidentally, bullets designed for penetrating heavy game animals like elephant - which need to penetrate very deeply and must therefore not tumble - have long, parallel sides and blunt round noses, just like early military rifle bullets.
Not all bullets tumble at the same rate. Other things being equal, small bullets will tumble more quickly than large ones, but the design of the bullet is also important; some visibly identical bullets will tumble at different speeds, generally depending on the internal construction. For example, the Yugoslavian bullet for the 7.62x39 has a lead core and has been found in tests to tumble much more quickly than the Russian steel-cored bullet in the same cartridge. Readiness to tumble may also be affected by how well-stabilised the bullet has been by the rifling. A well-stabilised bullet may pass straight through the target without having time to tumble. The original US Army .223 (5.56mm) 55 grain (3.56g) M193 bullet was notorious for rapid tumbling, but the current NATO 62 grain (4.02g) SS109/M855 bullet is fired from rifles with a much steeper rifling twist (1 turn in 7 inches - 18cm - instead of 1 in 12 - 30cm) and is more stable, to the benefit of long-range accuracy and penetration but at the cost of a slightly slower rate of tumble on impact. Various tricks have been used to increase the probability of a bullet tumbling; the British .303 Mk VII bullet had a lightweight tip filler with the weight concentrated towards the rear of the bullet, and the current Russian 5.45mm rifle bullet has a hollow tip.
If a bullet has a relatively weak jacket, the stresses of tumbling may cause it to break apart while it is travelling sideways through flesh - a process known as fragmentation - which further increases the wounding effect. Most 5.56x45 military bullets fragment, although they have to be travelling at high velocity to do so. This limits their maximum effectiveness to fairly short range, particularly from short-barrelled carbines which have a lower muzzle velocity. Most 7.62x51 NATO bullets do not fragment, although the German one does - by accident rather than design. Fragmentation is not an official requirement for any military bullets; if it were, there might be some legal challenge over the international prohibition on bullets designed to cause unnecessary suffering. The noses of hunting rifle bullets (and many commercial handgun bullets) are designed to expand on impact, which greatly increases the size of the wound channel. Such bullets are illegal for military use.