The problem with QE is that it gives incentives to engage in financial engineering and distorts the economy. Borrow at close to zero and buy an asset that yields a little bit more. Nothing productive is created. Why go out and create stuff when you can make more money doing a carry trade backed by the government?
Over the past decade low rates by the Fed gave people incentives to enter professions like mortgage brokers, real estate brokers, real estate speculators and finance professionals. It created over capacity throughout real estate and finance related sectors. Many of those people likely would have gone into professions that were more productive, were it not for artificially low rates. Now many of those people are out of work and its not their fault. Why do something productive when one can take make more money shuffling money from one place to the other? In the long run this will hurt the country.