The United States started applying Quantitative Easing in late 2008 when the economy was engulfed by recession. The short-term interest rates were hanging between zero and 0.25% that triggered the central bank to purchase long-term financial assets from commercial banks to stimulate the economy.  Ever since its inception, QE has been a controversial topic with equal share of supporters and detractors; garnering a variety of criticism from all pockets of the economic system.
Lowering the value of the currency
A common criticism that QE has repeatedly received is its ability to bring a drop in the value of the currency which is true as well. Each time a dollar is added to the economy, the value of the existing dollar sees a slight descent. Thus, the trillions that have been already added to the monetary base will only scathe the dollar. 
QE does not fuel credit
QE is brought to use, necessarily, to encourage spending and lending in the market. However, it has also been observed that the money that commercial banks receive from the sale of financial assets isn’t always put to use in lending. Many banks hold onto these funds to improve their credit, and are afraid of lending it. The demerit in this case is that banks can choose to not loan money to businesses or households. Plus, in the case of a liquidity trap, a bank may completely overlook lending because of the zero interest rate. There is also the possibility that there may not be a demand for loans either as a result of the unstable economy.
The perils of inflation
A very famous criticism tagged with QE is that of inflation. Based on estimations, it was feared that it can lead to inflation. It came to reality in 2011 in the United Kingdom when an analysis by the Bank of England estimated that inflation grew by 1.5 percent owing to QE, and resulted in damaged household’s disposable income.  It has also been observed that the combination of economic stagnation and QE over an extended period of time can add to the possibility of hyperinflation.  However, a study by the IMF in April 2013 also declared that QE is not likely to lead to inflation unless there are inconsistencies in the process or the economy is over-stimulated, and even then the effects are expected to be only minor. 
Potential deflationary effects
Deflation is another one of the accusations that QE has faced over the years. When a given economy is stuck in a Liquidity Trap then QE can cause deflation as well.
QE has also been criticized by BRIC countries under the banner that QE is a form of Protectionism and Currency War/Competitive Devaluation. 
- The Downside of Quantitative Easing by Daniel L. Thornton
- How Exact Could Quantitative Easing Cause “Unanchored” Inflation Expectations by Alexander C. Huberts (2013)