Re: @Loyal Commenter
"But what would prevent the Swedes dropping/postponing their case if the US put in an extradition request on much more serious charges?"
Within the law, or outside it? As long as the case is ongoing, all other requests are put on hold. There's also grace periods after the case is closed, and so forth. IANAL. WITHIN the law he's pretty well protected.
Outside the legal system? Nothing what so ever prevents them from just shipping him off. Except, of course, the "whops, you broke the law in full view of the international media" bit.