The liquidity injected is supposed to be taken out later, thus removing the inflationary distortion. Whether it will or not is anyone's guess. 2008's injections have yet to be taken out.
Central banks are easier creditors because, while autonomous, they are the same country as the government! So it's technically like owing yourself money. A central bank that cooperates with the debtor country (itself) would never force a default, and is thus never an acute problem. Of course, infinite money printing should lead to dangerous inflation.
The bad news is that by ignoring inequality, they may be just causing it.
That doesn't sound surprising when all that injected money goes directly to banks instead of individuals.