Try to get it scanned with VCDS after a drive, or during if possible, as it will uncover a multitude of things.
For instance, whether the cambelt is fitted properly, whether the MAF is goosed, whether it's remapped, whether any crash shutdown messages are stored (assuming they weren't cleared, I found a couple like this when looking meaning airbags had deployed), coolant sensors, and numerous other bits.
If you havent got VCDS, and you're serious about an S3 purchase and have a laptop you can utilise, I'd even say it is worth buying beforehand! A suitable quality cable and the software licence can be had for the same price as a couple of tanks of fuel.