I can't claim to be a regular reader of the Washington Post, but I certainly think it's a superior newspaper to the Washington Times - not for its liberal slant, but just because of its reputation for strong investigation and quality reporting. Kind of sad indeed that Scalia should find it too "shrilly" liberal, although I dare say someone of his calibre won't much suffer from the lack of extra perspective. Lesser thinkers will, though.
I should think so. I mostly just read the Economist and a Belgian newspaper (for national news), and occasional things here and there. To be sure even the Economist has its own outlook on things, but not really of the kind that requires much balancing, I think, and their international scope helps to see things in perspective and not get so hung up on a narrow set of topics.