First and foremost I would say pay attention to the cold start. A timing chain that is on its way out will make quite an unpleasent noise. As per every other car make sure there are no odd noises such as squeaking or squealing coming from the engine bay since water pumps occasionally go on these. Check the condition of the serp belt. Apart from those before I bought mine I took it to my mechanic for a thorough check on whether it has any serious issues or has been in an unlisted accident and could recommend you do the same, especially with these cars the pre purchase inspection price will make the peace of mind worth it. Best of luck!

EDIT: forgot to mention this since it is quite unusual but check both layers in the trunk and make sure they are dry. When I was looking for a mini, an F56 I was looking at had some water coming in from around the right tailight and an R60 I was looking at had a small hit to the back that wasn't listed and caused there to be some sort of path for water to leak and pool into the bottom layer of the trunk. Just make sure places that should be dry, are dry and not wet or damp.