1.) Maintenance records.
2.) How it drives, should be tight and without a floaty feeling. Also shouldn't have any creaks, groans, vibrations, rattles, etc.
3.) Maintenance records.
4.) How the engine sounds, no rattles, squeals, groans, etc.
5.) Maintenance records.
6.) Condition of the interior. Should be obvious.
7.) Maintenance records.
8.) Condition of the exterior. Should be obvious, no rust. Tires should have good life left in them.
9.) Maintenance records.
Whatever you do and no matter which E46 you buy, reserve ~$500 for maintenance expenses that will come up within the first 6 months to a year you own the car. You will have to change all driveline fluids immediately because it's likely never been done. Also, engine oil should be changed immediately just for good measure. This is especially true if you aren't buying the car from a BMW shop.
Did I mention the car should have maintenance records?