Walk in there with a scan tool of some sort. Carly for BMW and a bluetooth reader can get you a bunch of information about the vehicle, such as all its readiness monitors and live readings. A more advanced code reader can do the same for a more generalized used.

Check for paint work and prior body work. Bad repairs can hide rust that will break out in the future. Body work is not a normal DIY job, so I'd run away from any sort of rust.

Electrical drains are also not very fun to diagnose. If there is any drain issue that has been disclosed, or a lot of aftermarket electrical work done, I'd be wary. If harnesses and adapters weren't used, you could be chasing down a lot of cut wires and have to re-pin a lot of harnesses back to the factory plugs. No fun at all.

The mechanical stuff I'm sure everybody else will cover. But these are the things I look for first, as mechanic stuff is easier to fix than the stuff I listed.

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