I've owned a 2002 E46 330i. Things to check:
- Signs of rust around rear wheel arches.
- Gearbox (Manual) Check the spring detent works properly, and there is no stiffness or heaviness. If so, there is a cheap kit available to fix this (as I found out).
- Check for signs of water/mould in rear lights on boot-lid.
- Clunking or knocking due to suspension bushes.
- Check front fog/spot light surrounds are in place.
- Ask if radiator plastic fill tank has been replaced yet. They can crack suddenly usually after 130,000km (lots of steam gets out)
Otherwise they are bullet proof, but thirsty. Good luck they are great cars.