You have to be really careful with brand-new tires, too! A few years ago I bought some Pirellis for my Integra, and a neighbor helped me put them on. I asked him if he wanted to "go for a spin," and that's exactly what we did!
A couple miles into the drive, I found a nice wide patch of road and did some S turns, enjoying the nice handling of the 40 series tires (I think I was coming from 50's), when I totally lost it! I was going about 50 mph, and I did a complete 720 spin--really, really scary. Fortunately there was no one around, and the road was wide so it was a "free" learning experience.
Now I baby a car for the first hundred miles until that tire mold release compound is 100% gone. I can't imagine how bad this guy's Armor-All tires must have been!