Not trying to blow-the-whistle, just curious as to the laws.:)
~~Company "A" has employees working for 3 or 4 years. Then finds out that said employees' Social Security card numbers have come up invalid.

Said-employees leave for a couple days, come back with new Soc Sec Card and a new name.
Company "A" knowingly rehires them under the new name and number! Even accepting a "new" drivers license etc.
In the past year or more...Company "A" has gotten a tiny bit better, thanks to the new methods they have of screening, but still seems questionable to me.

Thanks for your input!

It's not how I would handle it. But if the company has reason to believe that the new numbers are now the valid ones there is nothing in the law to prevent them being rehired.

Company "A" knows it's not accurate.
Running joke is "What's your name this month"?

The problem is, Company A is walking a very fine line between a couple of different laws.

The law does not require them to be experts at determining what is a legitimate piece of ID or not. If they appear to be legitimate, they are more or less obligated to accept it as such.

They also are prohibited by law from discriminating on the basis of national origin. Having stricter requirements for I-9 documentation for some employees could definitely violate that law.

If Company A is smart, they're not keeping photocopies of the ID they are shown. They are not required to under the law; the law only states that IF you keep copies, you have to keep them for everyone. If they don't keep the copies, then if investigated all they have to do is say that the documentation appeared to be legit when shown, and the USCIS can't prove otherwise. Even if they do keep copies, unless the flaws are VERY evident, the worst that will happen is that they'll get a slap on the wrist and told to be more careful.

Honestly? Even if this is reported, this is going to be very, very, very low priority for your local USCIS office. They've got much bigger issues to worry about than this just now.