Unfortunately talc isn't the only mineral that can contain asbestos. Mica can too, as can Kaolin iirc. All mined minerals can be contaminated. What you need to look out for is responsible mining practices and quality testing.
With regards to cornstarch, it can cause terrible break outs and allergic reactions if the formulation does not have an effective enough preservative in because asa you can imagine bacteria will feed on it. Preservatives in cosmetics come with other health concerns. Some have hormonal effects and cross the skin barrier which is a risk concerning cancers. Some cause sensitivity and allergic reactions, some are harmful to the lungs if breathed in.
So my conclusion is to look at the statements cosmetic companies give regarding mining practices and the safety of their ingredients (and cross reference) and make your decisions from there.