Based on the article, it looks like the law is targeting all cash transactions for second hand items. Criminals usually don't pawn stolen items at trading posts, flea markets, antique stores, etc., yet this law will affect those types of businesses.
If the law should exist at all, then I think it should be narrowly tailored so as to effect those merchants which most often receive stolen goods, such as pawn shops.
But, even then, there are less restrictive and generally better means of reaching their goal. Why not make merchants keep logs of items bought/sold via cash? These logs could include the buyer's/seller's contact information so that if any wrongdoing is found or otherwise assumed to exist, then the person is easy to find. You can have a paper trail without restricting the types of payment accepted.
I don't see how requiring the use of money orders and cashier's checks will achieve their desired goal. Money orders don't indicate who the payment is from, and you can put any name for the payer on a cashier's check; these forms of payment could be just as virtually untraceable as cash.