My theory is that the administration wanted more stimulus, couldn't make it happen politically in useful ways (infrastructure projects, school building, new nuke plants etc), so the only outlet they had was QE, which did the job somewhat (we're not in a great depression), but did have the negative effects you highlighted. I think we'd be better off had the money been spent on infrastructure projects -- same sugar rush preventing a crash, plus we get a bunch of stuff afterwards. Right now we just have paper assets in the aftermath.
"Couldn't make it happen politically?!" That part I don't get. You mean they couldn't just give everyone money so they spend it instead of giving money more or less directly to the richest people? You mean the citizens would revolt?!
(Actually the possibility of QE on the scale we had in a bunch of democracies left me dumbfounded. Why do people put up with that shit?)
Politically, citizens have nothing to do with it, look at Congress. They're voted in on fears of socialism and kenyans, not like they can turn around and support infrastructure spending.
Also - what do you mean "credit is tight for businesses"? Haven't businesses of all kinds been vigorously buying back their stocks lately, while issuing bonds at the same time? Those bonds having very low yields?
Maybe grandma has a problem getting a loan from a bank to run her small shop (why would the bank lend out money when they get risk-free handouts from governments?.. AFAIK banks are actually notoriously bad at credit risk assessment when giving out loans to businesses so they tend to not bother); but definitely a public company issuing bonds has no problem of prohibitively high yields.
Another big issue is all the stuff that got financed that normally couldn't be financed, with investors everywhere willing to buy junk bonds and any imaginable kind of stock. How that works out remains to be seen.
(Personally I don't have a firm opinion on stimulus/austerity, apart from it being a far from obvious issue - that I believe rather firmly.)