One problem related to engine cooling system has been reported for the 2001 BMW 740. The most recently reported issues are listed below.
In April 2008 low coolant warning caused me open hood and add coolant. The coolant level was perfect but I still added more. The light for low coolant was still appearing every time I drove the car. Every preventive maintenance has been done by book on this BMW. The car has been to the dealer twice after this low coolant light but not for the coolant related service. They could have checked this and advised me of potential problem. Car has 65,000 miles. Plastic was found hardened by heat and brittleness cracked the same. 385 other BMW 740il owners have filed petition on internet for same cracked plastic radiators (on BMW 740i ,and IL models between years 1995 through 2001. BMW ignored our pleas for free replacement. Major safety issue not expected on premium car like this.