When taking over a lease (BMW), what due diligence should I do?

I would explore how much it would cost for an inspection if you’re going to the dealership anyway. It’s basically a quick visual check with it up in the air, plus some other basic checks like oil, etc and can’t be that expensive. If you’re having it inspected you should be able to have a service manager write that there’s nothing visually wrong with the vehicle based on the inspection which holds some weight.

For the disposition fee they normally waive it if you’re buying/leasing another car with them but needs to be in place at handover. It’s part of the BMW contract so no way to negotiate it unless either the original lessee gives you the money to offset it or you take another BMW financial product like a lease or loan at the end of this lease.