Season the pork with salt, smoked paprika, garlic powder and pepper and place it in a 6-quart slow cooker with the broth.
Cover and cook on low for 8 to 9 hours until the pork shreds easily and reaches at least 195°F for pull-apart texture.
Transfer the pork to a pan, discard large pieces of fat and shred with two forks.
Pour off the cooking liquid, return the pork to the cooker and stir in barbecue sauce and vinegar.
Heat on high for 15 minutes, then switch to warm and serve with slider buns and coleslaw if using.