In addition to these media covered cases, I have noticed cases of very old public domain works being seized by corporations with no involvement in their original creation.
So the solution to this, as with anything where getting caught and punished is infrequent and high costs are imposed on the victim, is to set damages high enough to make the expected return from this strategy non-positive.
If they owed $100k every time they made a false takedown, they'd probably be a lot more careful in the future.
I agree with you that harsh penalties for blatantly false copyright claims done in bad faith would help greatly. However there is a much larger problem in that the victims of these scams are small regular guy artists and content creators and the scam perpetrators are multi-billion dollar media organizations that control the media that advocates for new laws and have the congress, who ignores "small person feedback" in their back pocket with their SuperPAC and other bribery schemes/"campaign financing". How to solve that problem is the one that keeps coming up. Despite many realizing what a problem this situation is and discussion going on about it for many years, things only get worse, such as with the Supreme Court's Citizen United Ruling in 2010.
This isn't a DMCA takedown, it's a system Google put in place to avoid being sued by lots of copyright holders. $100k is nothing compared to the $1B lawsuit Viacom already filed, and other companies will have no problem filing similar lawsuits if Youtube doesn't toe the line.
Previous cases:
http://njnnetwork.com/2009/10/associated-press-and-fox-news-...
http://c4sif.org/2012/02/youtube-identifies-birdsong-as-copy...
http://productforums.google.com/forum/#!category-topic/youtu...
http://www.hollywoodreporter.com/thr-esq/megaupload-youtube-...
In addition to these media covered cases, I have noticed cases of very old public domain works being seized by corporations with no involvement in their original creation.