To increase the accuracy of slugs in a shotgun, purchase shotgun barrels or chokes that are rifled - these are becoming increasingly popular and do an excellent job in harvesting game at reasonable ranges.
A saboted slug is designed to be fired from rifled barreled shotguns or shotguns with a rifled choke tube. As the saboted slug exits the shotgun muzzle, the sabot is separated from the slug and falls away, allowing the slug to continue down range unimpeded. This type of shotgun ammunition is very accurate and provides plenty of knockdown power for most big game at ranges up to 150 yds.
The Foster Slug is used for hunting targets at longer distances. The hollow rear on this slug pushes its center of gravity toward the front, which in turn gives it greater stability, up to a distance of 75 yards. Most will feature small fins toward the rear, called "rifling".
Shotgun slugs are generally required to be used when hunting in built-up or semi-rural areas. In these areas, it would be unsafe to discharge center fire high power rifle cartridges that are capable of firing bullets that can travel distances greater than 2.5 miles.
The chart below shows how far shot and slugs from a shotgun can potentially travel.