Yes, get an independent PPI inspection. DO NOT rely on the CPO for any protection whatsoever. It is an extended warranty and THAT ALL.

Transmissions are a point of concern. Prior accidents, repairs, issues not fully fixed, etc, are always concerns. Demand a copy of the BMW Service history (without any prior owners names, just visits and service codes).

Did the insurance add the tax, title and other fees on top of the agreed upon value? They owe you for any costs to get a new vehicle- including the tax you will pay and the fees to license.....