Do non-retina graphics looks worse on a retina display than they did before? There are complaints that non-retina apps look terrible compared to retina apps on a retina iPad.

Is this purely in comparison with high-resolution apps, or does it actually look worse than it did on an iPad without the retina display, i.e. do four pixels forming one big virtual pixel on a retina display look worse than one big pixel of the exact same size on the old display?
Not to me - it probably looks worse because you are seeing the difference now more readily. Subjectively things look worse because you now expect a new-iPad level display. I had this effect when iPhone 4 came out, everything looked fine until I saw one.

It's not just the increased resolution that has improved - the maximum brightness of the new iPad display is brighter and the minimum brightness is dimmer. Dan Frakes noted this in MacWorld on March 30 2012 and it is important - the screen does look better if you can adjust the brightness to the right level, bright in the sunlight and dim when you're reading in the dark. Given that I say that non-retina graphics should in fact look better on the new iPad display when greater ability to adjust brightness matters.

I don't know if you ever played Marathon for Mac, late 90's game. State of the art graphics in its day, but now it's hard to tolerate when you play it on a modern machine. Not because it looks worse on a modern LCD but because you expect so much more.

(if you're interested - get the Marathon trilogy for Mac OS X - a GPL'ed release by Bungie)

With computers, you truly never can go back.