While Twilight vampires are extremely hardy, they are not invulnerable.
One of the justifications for their "humans must not know we are real" rule is that weapon development was reaching a point where they could be a threat.
While an easy interpretation for this would be missiles and nukes, it should be taken into account that this rule is a few hundred years old. You can interpret from this that while "all gunpowder weapons" are not a threat (see quote in Adamant's answer), sufficiently powerful ones may be considered a threat. Perhaps in the beginning it was just cannon and explosives, but with more powerful, efficient, and precise firearms, the larger handheld weapons (such as the .50 caliber mentioned in the question) would be a threat.
In the vampire vs vampire fights in the novels, most damage is done by physical force delivered by some form of martial arts. I think there was some mention of biting, but it was primarily brute force. Losers were dismembered and burned, which could point to flamethrower weapons also being a threat.
The activity of burning a vampire after dismemberment would seem to show that reattachment would be possible. So the physical trauma is to subdue the opponent with the fire to finish the job.
The speed at which the burning is performed would point to a rapid recovery time.