The greatest amount of error in a measurement would occur if the ammeter is inserted at point A. This is because inserting an ammeter in series with a resistor will change the total resistance of the circuit and affect the current flow throughout the circuit. In contrast, connecting a voltmeter between two points only measures the potential difference between those two points and does not significantly affect the circuit. Therefore, options A and E would not create a significant error, and options B and C would create some error, but not as much as option D.