One problem related to transmission solenoid has been reported for the 2006 BMW 750. The most recently reported issues are listed below.
Pre-owned vehicle -transmission issue which is not mechanical. . . Vehicle did not shift to reverse from park. Local BMW dealer says new transmission is needed. Research indicates it to be a problem with the vehicle electronics (solenoid) which sends shift signal to the transmission. BMW will not say this is an inherent issue with its product as evidenced by the number of similar complaints. When vehicle is in motion on any roadway at 40-55 mph, a series of fault codes are displayed on the dashboard [transmission fault-drive moderately], and subsequently the vehicle will stall and not engage into gear. Efforts to prove that this is not owner/consumer responsibility due to the internal nature of the fault(s) are not accepted by the BMW dealer/company. The cost of company stated repairs ($3500-$8000) are beyond what the value of the vehicle is and financial ability to pay.