Jech: If you have a micrometer, measure the dimensions of the finished bullets and confirm they are sized correctly. Otherwise, if they pass the size and visual inspection, use 'em. If in doubt as to their lube or content, a coating of liquid ALOX lube will help out.
As to zinc:
When I start a new melt, I start the cold pot with weights that I know for sure are lead weights, not zinc. The older style, unpainted dull grey weights (especially the 2 oz or larger) are what I use to get going. I put a few handfulls of them in first, a couple of inches deep, and get the pot going on high. That way I know there's only lead. Then once it melts, I stabilize the temperature and start shoveling in the mixed weights. The zinc and iron weights and the clips will all float on the lead.
If you have some nice ones, you can do a quick check by either dropping them on a concrete surface (the zinc ones "ping", but be aware that if you drop a lead weight on the clip, it will ping too!) or by trying to cut them with side-cut pliers. Lead weights will cut, zinc ones will not. Obviously this is time consuming, which is why letting the pot sort them by melt temp is the easy way as long as you keep temps at around 700F or so.
I do dump my wheel weight buckets out on a work surface and hand sort before I put them in the pot. There's always lug nuts, tire valves, cig butts, and other trash that needs throwing away. Plus I pull out the stick on weights and separate them. Anything that I can tell is zinc or iron gets in the scrap bucket right off. It costs money to run the burner and dumping heat into a half a bucket of non-lead weights is a waste of energy.
But if I miss a few, I don't let it sweat me.
For all that zinc WILL contaminate the alloy, in all honesty, less than 1% of zinc will not harm the alloy to the point of being unusable. By adding tin you can offset the zinc if you get a weight or two melted. It's just a shame to waste tin to remedy zinc. Zinc does harden the alloy just not the same as antimony.
Zinc's problem is it turns to a thick grey sludge- kinda like oatmeal- and it will prevent the lead from flowing well or filling out the mould details. More heat will melt it, but the melt point of zinc is right at the point where lead will start giving off poisonous oxides.
I've seen on forums and at casting demos people worry about zinc, and point to a thick grey sludge on the melt. Usually it's lead oxides and tin drossing out. Run your pot too hot even without zinc, you will oxidize the surface and unless fluxed back in, you will have a lot of dross loss.