I shoot. I cast some of my own bullets. I will salvage Lead and Lead alloys when and where it makes sense to. Also, I know a bit about inorganic and organic chemistry, biology and some of the ways you may end up ingesting Lead and/or have heavy metals contaminate your work area. No one here thinks Lead and its compounds are completely safe to intake, do they?
The video maker is doing a couple of things I wouldn't do.
First, he is handling the materials in his KITCHEN. Inside his HOME. Bad idea, there will always be some escape of dust and droplets of wash water. Particularly, the old Lead chunks scrounged from berms at a range have Lead oxide and carbonate (possibly other Lead compounds as well) on exterior. These dust off, his house WILL have had some contamination by Lead and Lead compounds. The more he does this processing in his house, the more contamination will build up. I really hope he doesn't have small children, a toddler crawling around on his floors would be exposed to the dust and residues. PLEASE don't do this work inside an inhabited building, at the very least, go OUTSIDE.
Second, handling Lead and wash water with his BARE HANDS. Bad idea! Wear gloves and a particle mask!! ALWAYS!!!
Third, he is using food prep equipment to smelt Lead. HAVE DEDICATED EQUIPMENT for processing, and keep it SEPARATE FROM YOUR KITCHEN EQUIPMENT.
Fourth, he has no control of smelting temperature. As others have noted, his heat source can reach the boiling point of Lead, this is a particularly BAD THING to do, which greatly increases the contamination of the surrounding area. Additionally, if you are salvaging wheel weights, some of these are now made of Zinc. Zinc will ruin your alloy for bullet casting, but it melts at higher temperatures- Zinc wheel weights can be easily skimmed off the top of a melt IF THE TEMPERATURE IS NOT SO HIGH AS TO MELT THEM.
Fifth, the heavy metal contaminated wash water is not what his local sewage plant was designed to work on. Please be responsible with your waste. A method I would use? First, mix some bicarbonate of soda (baking soda) into the water, this should convert any soluble Lead compounds into the insoluble carbonate. Dry that water up in a safe place. Mix the dried residue with some cement mix and water, cast it into a disposable can, old ice cream pail or such, THEN put it into the trash headed for the landfill- Be ethical and perform as much of a "rendering safe" and immobilizing of any waste Lead or Lead compounds as a private individual can easily do.
Sixth, he isn't recycling the Copper, gilding metal/brass materials from the jackets. This is worth several times the value of the Lead, weight per weight! Penny wise, pound foolish.