Is it possible to get an accurate (say 0.05%) measurement of a resistor using the arduino,
No... I'm not sure about accuracy of the ADC... can check ATmega specs for that. But at 10-bits, the BEST resolution you can get at full-scale is 1/1023, which is 0.10%. At lower ADC readings the percentage resolution of one bit is of course, worse. As a measurement "instrument", I would not expect the Arduino ADC to be anywhere close to a real multimeter...