I have no idea how big of a problem false or fraudulent copyright claims are, but they are in fact already illegal under U.S. copyright law:
Section 506(c) [1]:
Fraudulent Copyright Notice. — Any person who, with fraudulent intent, places on any article a notice of copyright or words of the same purport that such person knows to be false, or who, with fraudulent intent, publicly distributes or imports for public distribution any article bearing such notice or words that such person knows to be false, shall be fined not more than $2,500.
Section 512(f) [2]:
Misrepresentations. - Any person who knowingly materially misrepresents under this section —
(1) that material or activity is infringing, or
(2) that material or activity was removed or disabled by mistake or misidentification,
shall be liable for any damages, including costs and attorneys' fees, incurred by the alleged infringer, by any copyright owner or copyright owner's authorized licensee, or by a service provider, who is injured by such misrepresentation, as the result of the service provider relying upon such misrepresentation in removing or disabling access to the material or activity claimed to be infringing, or in replacing the removed material or ceasing to disable access to it.
Can you point to a single instance of someone or some organization being successfully prosecuted for issuing a false or fraudulent DMCA take-down request? Yes, such requests are illegal under current law, but that law is never enforced. Part of the problem (in my, possibly uniformed, opinion) is that the legal standard is too high: you have to "knowingly" issue a false DMCA request, and that is a tough standard to prove in court. There is no penalty for shotgunning take-downs every which way and seeing what sticks (and saying "oops, my bad" for the ones that don't).
Why does issuing a DMCA counter-notification not automatically trigger an investigation by the FBI?
Then there is the problem that DMCA is woefully inadequate to deal with Fair Use. Fair Use is often cited inappropriately to justify unauthorized copying that does not rightfully fall under Fair Use exceptions. However. DMCA makes no such distinction, and it is up to the entity hosting the allegedly-infringing content (i.e., the one to which the DMCA notice is sent) to determine whether the content is actually infringing. Even when an unauthorized copy of a work passes each of the four parts of Fair Use test with flying colors, the DMCA takedown requester is still not in violation of the law you cited. So there is no disincentive to issuing spurious take-down requests.
Valid point. Question: When congress makes infringement a criminal matter, do you think false and fraudulent copyright claims should be treated a criminal matter (since they would be, essentially, false police reports)?
Previous discussion on HN has come to the conclusion that the false DMCA takedown prohibitions are effectively toothless because the adverbs used set an incredibly high bar of proof and malice.
Section 506(c) [1]:
Fraudulent Copyright Notice. — Any person who, with fraudulent intent, places on any article a notice of copyright or words of the same purport that such person knows to be false, or who, with fraudulent intent, publicly distributes or imports for public distribution any article bearing such notice or words that such person knows to be false, shall be fined not more than $2,500.
Section 512(f) [2]:
Misrepresentations. - Any person who knowingly materially misrepresents under this section —
(1) that material or activity is infringing, or
(2) that material or activity was removed or disabled by mistake or misidentification,
shall be liable for any damages, including costs and attorneys' fees, incurred by the alleged infringer, by any copyright owner or copyright owner's authorized licensee, or by a service provider, who is injured by such misrepresentation, as the result of the service provider relying upon such misrepresentation in removing or disabling access to the material or activity claimed to be infringing, or in replacing the removed material or ceasing to disable access to it.
[1]: http://www.copyright.gov/title17/92chap5.html#506
[2]: http://www.copyright.gov/title17/92chap5.html#512