1) What happens to the value of the dollar when new forms of money, like credit cards, are introduced? I expect you'd say that the value of the dollar would fall, but this means the credit card company is like a counterfeiter--which it isn't.
2) What happens when the Fed prints $100 and buys a $100 bond? I expect you'd say that is inflationary, but as the $100 cash is added to the aggregate spending power of the economy, the $100 bond is subtracted from it.
Start with the old quantity equation, MV = PY, where M is money, V is velocity, P is the price level, and Y is output. Define M as high-powered money, meaning the liabilities on the Fed's balance sheet.
In this framework, credit cards are not money. What credit cards do is raise V, by reducing the amount of high-powered money needed to satisfy the demand for transactions. To compensate for this higher V, the Fed might have to reduce the amount of M relative to what they would otherwise. As long as V changes gradually and predictably, this is not a problem.
In this framework, the Fed buying a $100 bond raises M. The seller of the bond does not have to feel $100 richer for the transaction to affect the price level. However, the bond purchase sets in motion a series of adjustments, the end result of which is that the price level is higher.
In this Monetary Walrasian story, it does not matter what type of bond the Fed purchases. Back in the real world, Ben Bernanke seems to think that buying mortgage-backed securities is different from buying Treasuries, and he thinks that the economy would be better served right now by having the Fed buy some MBS. That seems to harken back to the view that credit matters (it is not just money), which fits in with my Austro-Keynesian point of view.