People are already talking about bullet wounds, but what about splints? Maybe people with good enough first aid skill can fit them better, allowing the limb to recover a bit faster. I haven’t played much with npcs, but is it possible to apply bandages and splints to them yourself?
Also, it might be hard to apply intravenous drugs without knowing where your veins are, so injecting yourself with a syringe would take longer without some first aid skill, and you might even end up applying mutagenic serum incorrectly, taking damage, hurting your health, and getting bad mutations. I’m thinking this could also spread to applying inhalers and oxygen tanks, but I’ve never used them, so I’m not sure.