I don't know of any safety issues with a worn barrel; in theory, the chamber could move forward due to compression of the steel, but that is going to take a whole lot more ammo, and a lot higher pressure ammo, than would be needed to wear out the barrel. If the rifle has been fired enough to cause battering of the locking lugs and lug seats, then excess headspace is a consideration, but generally, barrel wear will happen first.
The result depends a lot on what type of barrel wear. Throat erosion will allow the bullet to tilt coming out of the case mouth and the damage to its base will ruin accuracy. Muzzle wear, usually caused by cleaning from the muzzle without a muzzle protector, will also allow the bullet to tip as it exits the muzzle, and accuracy will suffer.
How bad can accuracy (or lack of it) become? As trigger643 says, a sub-MOA rifle can become a 2-4 MOA; at worst, barrel wear/damage at the muzzle can result in "bushel basket" groups.
Jim