In an abstarct sense, Obama probably "won" the debate as performance art. But Romney surely seemed adequately Presidential and I doubt that Obama's Presidential petulance was attractive to any remaining undecideds.
However I am sure Obama's "zingers" gave Chris Matthews a tingle and helped fire up the many haters amongst the Democratic base. It is presumptuous of me to attempt to out-think the Democratic brain trust, but my guess is that Obama's hope was to goad Romney into a display of temper that would be immediately criticized by the Dem media chorus as racist. Yes, Romney was extremely unlikely to say "Stifle yourself, you uppity black boy" but the Dems were desperate to pretend he had and would have pounded any flash of Romney temper into that mold. Oh, well - that didn't work, so they will need something else to light their fire.
On the Detroit bailout, it is pretty clear that Obama's attack is on yet another Dem strawman; what Romney favored was restructuring, not a liquidation. In November 2008 Romney argued for private financing with some Federal guarantees rather than a full Federal bailout. Since private markets were essentially closed by the winter of 2009, one is left guessing whether Romney would have compromised with reality in favor of liquidation, or a full Federal bail out.