DNA in and of itself cannot be patented, as it is a product of nature. Biotech companies patent isolated portions of DNA that code one or more proteins. While such patents are admittedly controversial, they are a fairly small percentage of overall patents granted.
Re: Dr. Salk - your prior comment was clearly aimed at demonstrating how unpatented products can foster innovation, in support of your overarching point that the patent system is somehow broken. My point was that you (and many others that support abolishing the patent system or reforming it out of existence) is that patents also foster innovation. In some instances, they just accomplish that goal in a different way. Having worked for the government, a large patent firm, a small patent firm, as in house counsel, and as a patent law professor, I have some perspective on how patents are leveraged as business assets. I also understand how companies innovate around existing patent rights. You might be surprised to learn that those "design around" activites produce technological advances too. Sometimes more so than "good ol' collaboration."
As to your final point, I would argue that the reason so many patent applications are filed is because we live in an unprecedented age of technological growth. The shear magnitude of the technical evolution that has taken place in the past 100 years (and the past 30 in particular) has been nothing short of staggering. My grandmother grew up in an age where horse and buggy travel was still the primary means by which people moved from place to place. By the time she died (at the ripe old age of 99), humans had personal transportation systems (cars) that would take them across the US in a matter of days, group transport (e.g., planes) that could take them anywhere in the world in under a day, information distribution systems (e.g., computers, internet) that allow instantaneous access to information on innumerable topics, etc. In sum, there are a lot of patents filed because there is a lot of innovation taking place every single day.
Are there areas where the patent system could be improved? Certainly. I could rattle off a list 3-4 pages long off the top of my head. But the issues I would raise are largely concentrated in certain niche areas such as software, biotech, wireless communication, etc. But in my opinion, it is a long leap to extend problems isolated to those particular areas to the patent system as a whole.