Bumping to report another data point for the same problem. Radeon X1650 Pro, Windows XP, DirectX 9. I get all the same behavior described: messed up yield icons and citizen indicators in the city screen, and bad or missing icons in tech panels on the F6 screen. All these look like a texture is being shifted or scaled or cropped incorrectly. I also get those occasional moments when all the terrain goes gray and slowly redraws.
Looks like I'll be upgrading. The Radeon 6670 looks like a pretty sweet-spot budget card for Civ 5.