Corky opens the trunk through the missing rear window, but from the inside of the car it appears that the window is not missing.
Although it is central to a very funny and well-made segment, there is no way in reality that a taxi driver as incompetent as Helmut could have gained a license.
This film takes place sometime during the winter, and the opening story takes place in Los Angeles starting at 7:07 PM. At no time during the winter would Los Angeles be this sunny at 7:07 PM. In fact, the latest time of day the sun would set during the winter would be at 6:07 PM on March 20, the last day of winter. (Currently, March 20 would occur during Daylight Savings Time, but, in 1991, Daylight Savings Time did not begin until April.)
Cameras and studio lights are very visible in the sunglasses of the drivers in Los Angeles and Rome.
In the Rome segment you can see several times a black car following the cab, probably the production crew.