So the Fed has abut 1.7 trillion in MBS right now. I suspect as you do that they did buy a lot of crap well above market back in 2009-2010, but over time, the economic recovery (and the low rates, and the rising property values, and the inevitable sales and refinancings and interest payments) covered a multitude of sins and if I had to guess, most of their stuff has actually made them money.
They get about 200-250 billion in principal repayments every year for their 1.7 trillion portfolio. Based on that number, I'd guess that the majority of MBS they bought back in 2009 has already shuffled off the balance sheet at this point, the likely losses mixed in with the interest payments. And remember those bubble-year interest payments are a whole lot higher than payments are today, so it might have even been a moneymaker all things considered, since they managed to engineer a housing re-bounce as well as keep rates insanely low – which drove refinancing, which helped the Fed rotate that stuff off the balance sheet, etc.
I'm relatively sure its all good right now. In 2010, I'm also relatively sure it was NOT all good.
Of course, if RE tips over here, its unlikely this miracle will work a second time. There's no more space to engineer rates lower than 3.5%. I'm not sure what happens when the Fed is shown to be insolvent during that hypothetical future crisis. Its probably not great for the dollar, and it certainly will end up dropping the remit to the treasury. How long could the Fed extend-and-pretend? Audit-the-Fed might end up blowing up the buck.